This question refers to the differences which exist between the Holy Prophet (S) and other people. In fact, it does not concern the general differences between men and women in the way they have sexual relationships with each other.
In a nutshell, we should say that:
1- The privileges given to the Prophet (S) are for the obligations which have been put exclusively on him.
2- The Prophet (S) never went to extremes in making use of these rights and privileges.
3- As per Shia belief about the permissibility of fixed-time marriage, there is not any difference between the Prophet (S) and other men in terms of the number of women they can marry?
4- Although the limitations and restrictions applied to the Holy Prophet’s wives were associated with their status, yet they were not forced to live with the Prophet (s). In fact, they accepted these limitations of their own consent and choice.
The above question can be answered in several parts which are as follows:
1. Do all those cases which have been pointed in verse 50 of Sura al-Ahzab concern the Prophet (S) exclusively?
2. Why was a special kind of marriage particular to the Prophet (S) in the sense that the believing women could dedicate themselves to the Prophet (S) and be married to him without receiving dowry (mahr)?
3. Why did the Prophet (S) enjoy special privileges in sexual matters as compared to other men?
4. In spite of all these privileges for the person of the Holy Prophet (S), why were his wives deprived of the rights of an ordinary woman? In other words, why were they not allowed to marry another man after the demise of the Prophet (S)?
Now we shall deal with the above questions in the same order in which they appeared above:
1. First of all, it is necessary to give a look at the verse in connection with the first part of your question. God, the Exalted, says to the Holy Prophet (S) in the said verses:
"يا أَيُّهَا النَّبِيُّ إِنَّا أَحْلَلْنا لَكَ أَزْواجَكَ اللاَّتي آتَيْتَ أُجُورَهُنَّ وَ ما مَلَكَتْ يَمينُكَ مِمَّا أَفاءَ اللَّهُ عَلَيْكَ وَ بَناتِ عَمِّكَ وَ بَناتِ عَمَّاتِكَ وَ بَناتِ خالِكَ وَ بَناتِ خالاتِكَ اللاَّتي هاجَرْنَ مَعَكَ وَ امْرَأَةً مُؤْمِنَةً إِنْ وَهَبَتْ نَفْسَها لِلنَّبِيِّ إِنْ أَرادَ النَّبِيُّ أَنْ يَسْتَنْكِحَها خالِصَةً لَكَ مِنْ دُونِ الْمُؤْمِنين." 
“O Prophet! surely We have made lawful to you your wives whom you have given their dowries, and those whom your right hand possesses out of those whom Allah has given to you as prisoners of war, and the daughters of your paternal uncles and the daughters of your paternal aunts, and the daughters of your maternal uncles and the daughters of your maternal aunts who fled with you; and a believing woman if she gave herself to the Prophet, if the Prophet desired to marry her-- specially for you, not for the (rest of) believers; We know what We have ordained for them concerning their wives and those whom their right hands possess in order that no blame may attach to you; and Allah is Forgiving, Merciful.” 
Whoever has even little knowledge of Shari’ah law knows that the women mentioned in this verse are not lawful exclusively for the Prophet (S) except for once case. They are lawful for all people and the sentence “We have made lawful to you” does not imply exclusivity; rather there are also other verses which are addressed to the Prophet (S) but the injunctions in those verses include all Muslims alike.
2. The only case which is particular to the Prophet (S) is where a woman gives or dedicates herself to the Apostle of God (S) volitionally and with her own consent. Marriage with such a woman is prerogative of the Prophet (S) and others have no right to it. However, if we look carefully at this part of the verse, we will come to a very interesting conclusion at the end:
Firstly, this method is not practically a way to provide a real monopoly for the Prophet (S); rather if a woman refers to other individuals as well and expresses his willingness for marriage with them, there is the possibility of marriage to take place. The only difference is that the Prophet (S) could marry her without paying a dowry whereas if others are to marry her, it is necessary for the husband to pay a dowry.
Secondly, some exegetes of the Holy Quran are of the view that the Prophet (S) never benefitted from this exclusive right but there is a group of exegetes who believe that only one woman married the Prophet (S) in this way. According to some reports, she was a widow or a divorced woman with a child named Sharik.
We, therefore, cannot consider this method of marriage, an extraordinary privilege for the Prophet (S) nor can we say that it is an indication of the Prophet’s freedom to gratify his sexual needs.
3- As for why men in general can choose up to four wives,while there is not such a restriction for the Holy Prophet (S), we must say that:
1-3. The privileges given to the Prophet (S) are for the obligations which have been put exclusively on him. That is why we see that if the Prophet (S) has been given a privilege in one case, in another case he has been obligated to do a certain act of worship (such as the Tahajjud Prayer) as an exclusive duty of his. Tahajjud or the night prayer is an obligatory prayer for the Holy Prophet but it is a recommend act for others and they will not be punished for not offering it.
Some believe that since that Holy Prophet (S) was at the peak of irfan (Gnostic relations) with God and on the hand he was bound to live a normal life with ordinary people, therefore he needed some adjusting media (means) of which associating with the wives was considered to be one.
2-3. A study of the history shows the establishment of harems with dozens and sometimes hundreds of concubines kept by the rulers but the Prophet (S), despite theoretically being allowed to have such a harem, as per the most famous report, did not, in practice, have wives more than the number of the fingers. Among his wives only one of them was a girl, the rest were either widows or divorced women. All of this shows that sexual gratification was not the only motive behind the Prophet’s marriages.
3-3. According to Shia, apart from the Holy Prophet (S) other men are also not faced with any constraints about the number of wives they can have. However, only four wives can be permanent and the rest, if any, should be married through temporary marriage contract.
4-3. Regardless of some natural differences among the wives, you cannot find an instance where one of the Prophet’s wives may have complained about her sexual needs not being met. In other words, all the Prophet’s wives were happy and content with the situation they were in. As shall be mentioned, none of the Prophet’s wives wanted to separate from him. However, we can rarely see any individuals who may treat their wives justly in terms of meeting and satisfying their sexual needs. It is for the same reason that the limitations in terms of the number of wives they can marry shall be justifiable.
4. Regarding the last part of your question, we must say that the differences existing between the Prophet’s sexual freedom and his wives refer to one of the following two cases:
1-4. A part of these differences originates in the differences which exist naturally among men and women and which are not particular to the Prophet (S). The reason has been provided in its respective place. Although this part of the answer does not directly deal with your question, you can refer, in that connection, to the relevant answers in the footnote. 
It should be note also that the Prophet’s sexual relationships with his wives, insofar as they are live, are not different with other men, thus the same limitations which apply to other women also apply to the Prophet’s wives.
2-4. The second part has something to do with the differences existing between the Prophet’s wives and other women. In this regard, it is necessary to mention that owing to the high status of the Prophet’s wives in society, they could not behave in the way the ordinary women behaved. God says to them:
“O wives of the Prophet! you are not like any other of the women; If you will be on your guard, then be not soft in (your) speech, lest he in whose heart is a disease yearn; and speak a good word.” 
“O wives of the prophet! whoever of you commits an open indecency, the punishment shall be increased to her doubly; and this is easy to Allah.” 
Attaining such an important status and being entitled as the mothers of the faithful cannot happen forcefully and without their personal consent.
It is for the same reason that God, the Exalted, advises the Holy Prophet (S) as such:
“O Prophet! Say to thy Consorts: "If it be that ye desire the life of this World, and its glitter,- then come! I will provide for your enjoyment and set you free in a handsome manner. But if ye seek Allah and His Messenger, and the Home of the Hereafter, verily Allah has prepared for the well-doers amongst you a great reward.” 
It was only then that the Prophet’s wives were allowed to choose between one of these two options:
First, if they are to separate from the Prophet (S), they can receive a valuable gift and separate from him very respectfully and then carry on their lives like other ladies. Naturally, if they were to choose this option, they could marry another man.
Second, considering their privileged worldly position and the suitable heavenly rewards which they receive, if they remained pious and God-fearing, they could still remain the Prophet’s wives.
Obviously, the second option is accompanied with some limitations also.
History stands witness to the fact that all of the Prophet’s wives preferred being with the Prophet (S) while being fully aware of the limitations and consequences of the marriage. According to a report, Aisha preceded others in declaring her consent and satisfaction.
One of the limitations for the Prophet’s wives was that they were not allowed to marry other men after the demise of the Prophet (S). It is clearly stated in verse 53 of Chapter al-Ahzab which says:
“And it is not for you to cause annoyance to the messenger of Allah, nor that ye should ever marry his wives after him. Lo! that in Allah's sight would be an enormity.”
Ibn Abbas says that this verse was revealed about a man who wanted to marry Aisha after the demise the Holy Prophet (S). Another commentator named Al-Saddi says that the man who wished to marry Aisha was Talha bin Ubaidullah.
Note that Talha was the very man who, with the support of the Mother of the Faithful, created a big mischief that resulted in the bloody Battle of Jamal. Now, if he would marry the Mother of the Faithful, what would happen? There is no doubt that he would create greater seditions and mischief in the land as the husband of a woman who was a former wife of the Prophet (S). He would steer the public mind or the common sense to justify his evil deeds.
It was for this and many other reasons that others were not allowed to approach the Prophet’s wives for marriage after the Holy Prophet’s demise. As was mentioned earlier, the Prophet’s wives were allowed to separate from him and marry another man during his lifetime but since they chose, of their own consent, to stay married to him, they also implicitly accepted the limitations.
 - Al-Ahzab, 50.
 - Translated by Shakir
 - See for instance: Sura Talaq (divorce) verse 1.
 - Kulayni, Muhammad bin Ya’qub, Al-Kafi, vol.5, pg. 384, hadith 2, Dar al-Kutub al-Islamiyah, Tehran, 1365 (1986) A.H.
 - Tabari, Abu Ja’far Muhammad bin Jarir, Jami’ul Bayan fi Tafsir al-Quran, vol.22, pg. 17, Darul Ma’refah, Beirut, 1412 A.H.
 - Majlisi, Muhammad Baqir, Behar al-Anwar, vol.22, pg. 202, Al-Wafa Institute, Beirut, 1404 A.H.
 - In this regard, you can refer to different exegetic (commentary) books under the third verse of Sura al-Nisa.
 - Al-Isra, 79.
 - Kulayni, Muhammad bin Ya’qub, Al-Kafi,pg. 5, pg. 451.
 - Indexes: “The difference in the blood money for Man and Woman” No. 2207; “The Difference between Man’s Blood Money and Woman’s”, No. 2379; “The Philosophy of the Difference in the Ruling Applied to A Female and Male Apostate,” No. 1912; “The Reason behind the Difference in the Blood Money of Man and Woman”, No. 7469; “The Difference in the Inheritance of Man and Woman”, No. 886.
 - Al-Ahzab, 32.
 - Al-Ahzab, 30.
 - Al-Ahzab, 28 – 29.
 - Tabari, Abu Ja’far Muhammad bin Jarir, Jame’ul Bayan fi Tafsir al-Quran, vol.21, pg. 100.
 -Ibn Kathir al-Damishqi, Tafsir al-Quran, al-Azim, vol.6, pg. 403, Dar al-Kutub al-Ilmiyah, Beirut, 1419 A.H.