Murder can be studied and classified into different categories from different perspectives which we shall mention as under:
1. Justified and unjustified murder;
2. Time of murder;
3. Murder through implementation of capital punishment such execution, hanging, stoning and various other kinds of carrying out death punishment;
4. Intentional and unintentional murder or voluntary and involuntary murder. We guess your question is about the last category of murder.
Your question is very general and it is not clear as to what kind of murder you exactly mean and which category your question refers to. A question must be precise, clear and specific so that it may be given an appropriate answer. For example, it is not rational to ask a question about different kinds or categories of human beings because humans can be divided from different aspects such as religion, race, colors, sex, citizenship, age, location and a lot of other factors.
The same is true with murder or homicide which can be divided into many kinds from different aspects. We will explain some of the various kinds of murder as under:
1. Justified and unjustified murder: The killing of people, who are legally sentenced to death due to a crime whose punishment is death or the killing of infidels and disbelievers who are in a war with the Islamic country, or the killing of people, who are Muslims apparently but launch an armed rebellion against the Islamic government, is justified. The killing of people other than these is considered to be unjustified.
2. Time of murder: Murder is divisible in terms of the time in which it takes place because he who commits murder (let's say manslaughter) in a haraam month gets a severer punishment than when he commits it in other months.
3. Murder can be classified in terms of the methods of implementing a death penalty. There are different ways a death penalty can be carried out. They include execution, hanging, stoning etc.
4. Murder in terms of how the murderer is dealt with: It is another category relating to murder. For instance, if a murderer is justified in killing someone, he will not be considered guilty, so he is not sentenced to any kind of punishment. However, at times the killing might take place without prior permission from or coordination with the Islamic state which disturbs the law and order situation. The unauthorized murder of people whose blood can be spilled also entails punishments. One who intentionally and deliberately murders an innocent person will be sentenced to death. At times, the family of the victim can pay money to the family of the murderer and appeal the court to carry out death penalty and in certain cases, there is no need for payment of money. Sometimes, the death penalty is changed into blood money (mulct) or the blood money is fixed in the first place. However, the amount of blood money differs from time to time. In most cases, it is the murderer himself who should pay the blood money. When a manslaughter or a pure involuntary murder takes place, it is the sane family members of the murderer who are under the obligation to pay the blood money. Such a payment is like general insurances.
5. Another important category of murder relates to how it takes place and the circumstances in which the murderer carries out the homicide. Most probably, your question refers to the same category. Hence, therefore, murder can be divided:
A) Intentional or voluntary murder: Regardless of the means of murder, the murderer embarks on killing an innocent person willfully and intentionally or he carry the means of murder to another person causing his death irrespective of whether or not he himself has the intention to kill him.
Normally, an intentional killing takes place with a person's direct involvement but in some cases, abstention from doing an act also might lead to intentional murder. For instance, if a nurse refrains from giving medicine or food to an admitted patient in hospital resulting in his death, she will be guilty of intentionally murdering him, although she did not do any action.
In an intentional murder, if the murdered person is a believer, it is possible that in addition to the punishment levied against him in this world, the murderer might abide in Hell permanently.
In the case of a deliberate murder, there can be one individual or many individuals (accessories) accused and considered guilty of a single crime.
When it comes to retaliation, it is necessary that similarity in religion, gender, freedom and captivity and the likes be taken into consideration.
B) Murder can be involuntary or criminally negligent. That is, a person commits a crime without having the intention to commit it. For example, a surgeon carries out a surgical operation which results in the death of the patient.
An involuntary criminally negligent murder is that when a person's act may result in anti-social result such as murder when in fact the perpetrator have been conscious and willful but the achieved result was never intended by him.
In a criminally negligent murder (manslaughter), the heirs cannot appeal for retaliation. They can ask for mulct (blood money) only.
C) A murder can be purely unintentional in the sense that the person who committed homicide did not intend to kill but the murder occurred accidentally. The example of purely unintentional murder would be if you shot at an animal and shot a person in the woods beyond the animal.
If an insane person or a minor intentionally kills a person, it will be regarded as accidental death and does not result in retaliation but their paternal relative should pay the mulct of death to the inheritors of the murdered. There are different ways to prove a murder. They are the confession of the murderer, testimony of witnesses and compurgation [method of trial in which a defendant is acquitted if a specific number of friends and family swear upon his/her innocence.]
As you can see, there are five categories of murder and there might be other categories which can be found through research in legal texts. Given the fact that there exists a very comprehensive classification of murders, especially about the last category, in jurisprudential books and legal works, it is not known which part is ambiguous to you. Therefore, given that you are a law student, it is good of you to clarify your question and make it further specific. If there is anything ambiguous, you can write back and we will give the answer in more details.
 - Khomeini, Rohullah, Tahrir al-Wasilah, vol.2, pg. 508 – 509, Dar-ul Ilm Publications, Qom, 2nd edition; and also article 206 the Islamic Criminal Code.
 - Al-Nisa, 93, (If a man kills a believer intentionally, his recompense is Hell, to abide therein (For ever): And the wrath and the curse of Allah are upon him, and a dreadful penalty is prepared for him.); Hurr Amili, Muhammad bin Hasan, Wasail al-Shi'ah, vol.29, pg. 31, narration No.35074, Aalulbayt (a.s.), Qom, 1409 A.H.; Tabatabai, Muhammad Hussein, Translation of Tafsir Al-Mizan, vol.5, pg. 62.
 - Article 212, Islamic Criminal Code.
 - Tahrir al-Wasilah, vol.2, pg. 554, issue No. 5; also, see: Article 295 of Iran's Islamic Criminal Code
 - Guldoziyan, Eraj, Private Criminal Law, Jihad Danishgahi Publications Institute, 6th edition, 1378 (1999), pg. 108.
 - Ibid, pg. 109
 - Tahrir al-Wasilah, vol.2, pg. 554, issue No.7. Also, see: Article 296, Islamic Criminal Code.
 - Article, 221, Islamic Criminal Code