Absolute existence has different meanings and usages; sometimes it means ‘unconditional’; that there is no condition limiting it, not even the condition of absoluteness (one of its conditions isn't absoluteness). Sometimes, this isn't the case, and although it is absolute, it is still limited to the condition of absoluteness (one of its conditions is absoluteness). Whenever it said that absolute existence is equal to actuality and externality, the first meaning is what is meant (that even absoluteness isn't one of its conditions).
On the other hand, when it is said that existence is either mental or external, nondual or multiple, or is potential or actual, what is meant is the existence whose condition is absoluteness, which in reality, is one of the degrees of existence.
The absolute existence is the subject of irfan, while existence in its absoluteness is the subject of philosophy.
The absolute existence, is the very essence of the Ever-Standing wajib al-wujud (i.e., the necessary being in and of itself), and what is meant by this being, is the individual existence whose quality is itlaqi (unconditional) oneness that isn't capable of being multiple and has no match in the realm of existence. Anything other than it is actually a reflection and manifestation of that one original being. Proponents of the absolute existence speak of an absolute existence stripped of any particularity whatsoever which is free of all conditions, an essence that cannot be limited by any conditions.
Existence in its absoluteness though, on the other hand, exists when even one instance of it takes on actuality, and ceases to exist when all instances of – both mental and external – cease to exist, while the absolute existence exists when the one true existence exists, and ceases to exist when that one true existence ceases to exist.
Related question: Question 4543 (website:4848).
 HasanZadeh Amoli, Hasan, Mumidd al-Himam, pg. 448, The Ministry of Culture Press, Tehran, first edition, 1999.
 Daamaad, Mir Mohammad Baqir, Jazavat va Mavaqite Matn 93 al-Jadhwah al-Taasi’ah Wujud Mutlaq, Mirase Maktub Press, first edition, Tehran, 2001.
 Ibn Tarakah, Tamhid al-Qawa’id, introduction by Seyed Jalal al-din Ashtiyani, Muqaddamah al-Tahqiq, pg. 1, 1981.
 Sajadi, Seyed Jafar, Farhange Ma’arefe Eslami, vol. 2, pg. 1245, Tehran University Press, third edition, 1994.
This question does not have a detailed answer.