Advaita Vedanta shares some terminology with the Madhyamaka systems, and thus appears to have many similarities. However, Shankara's system has many crucial differences:

The Conventional Self

Shankara asserts that the conventionally existent, empirical living self (jiva) is the combination of a passive observer consciousness (sakshin) and an active inner physical organ (antahkarana) that assumes the form of objects cognized. Before liberation (moksha), the two are always together, although in deep sleep, the observer consciousness withdraws into ignorance (avidya), which is each living self’s share of illusion (maya). Buddhism asserts that the conventionally existent self is imputable on the aggregates, but is not the combination of any of them.

The Relation between the Self and Either Brahma or Voidness

Shankara asserts that each observer consciousness is identical with nirguna brahman (brahman without qualities), and that with liberation, the inner physical organ associated with that observer consciousness returns to maya-illusion, and that the observer consciousness merges with brahman without qualities. If we look in Buddhism at the relation of the conventionally existent self and self-voidness (the absence of true existence), Buddhism never says that the two are identical, nor that they merge with liberation or enlightenment. Self-voidness is the manner in which the conventional self exists, namely devoid of existing as a truly existent self. As for a truly existent self, there is no such thing. If we analyze in terms of other-voidness, and take other-voidness to refer to the clear light mind, then although, in general, both the appearance of a non-truly existent self and of a truly existent self are the appearance aspects of the clear-light mind, they are not identical with the clear light mind. "Identical" in Buddhism means totally the same. Although with enlightenment there is no longer an appearance of a truly existent self, let alone a belief in one, that does not mean that the truly existent self has merged with the clear light mind. Also, even with enlightenment, there is still a non-truly existent imputable self.

Shankara asserts that maya-illusion is the potency (shakti) in the God Ishvara. Empirical reality, perceived publicly by all, is the creation of Ishvara (ishvara-srshta) and is the practical commonsense world (vyavaharika). Private reality, perceived individually, is the creation of each living self (jiva-srshta) and is the apparent world (pratibhasika). Both the empirical world and the various private worlds spring from maya-illusion. I have no idea how Shankara's concept of srshta (springing, creation) compares with the Chittamatra discussion of natal sources and alayavijnana. I doubt that they are the same.

Maya-illusion in Advaita is not like the Samkhya assertion of existent primal matter (prakrti), with all objects being illusory (maya) perturbations (vikara) of primal matter.

[See: Basic Tenets of the Samkhya and Yoga Schools]



According to Shankara, maya-illusion cannot be characterized as existent or nonexistent. Ignorance is when we confuse our private world with the public world. Objects perceived privately endure only so long as they are perceived by a particular living self, while objects perceived publicly endure even when no living self is perceiving them, since they are always perceived by Ishvara. Buddhism is very different from this, both in Chittamatra and Madhyamaka, as discussed above.



Space and Time

Shankara asserts that the various manifold living selves themselves, as well as maya-illusion itself, and Ishvara himself, are in neither space nor time. All publicly and privately perceived objects are in space and time, and space is in time. Time is what relates the various living selves and maya-illusion.

In Madhyamaka, time and space are not conceived as containers for objects. Time is a measurement of change, and space is the absence of anything tangible or obstructing that would prevent a material object from occupying three dimensions. Both time and space are devoid of true existence.

Nonduality

Brahman without qualities (nirguna brahman) displays or translates (vivarta, literally: turns) itself in the sphere of space and time as various objects springing from maya-illusion, as well as various individual living selves and Ishvara. However, brahman without qualities itself does not change. The unity (aikya) of all these diverse displays – in the sense of them all being displays springing from maya-illusion – is brahman with qualities (saguna brahma). Brahman without qualities, however, is nondual (advaita) in the sense of being beyond the differentiation of unity and diversity. Thus, Shankara's Advaita Vedanta theory is not the same as Ramanuja's Vishishta Vedanta theory of the evolution of maya-illusion and living selves from brahman as transformations (parinama) of it. Nor is it the same as the Kumarila's Purva Mimamsa theory of unity within diversity (bheda-abheda).

When Madhyamaka uses the argument of neither one nor many, this refers to the fact that if things were truly existent, such as the self and the aggregates, there would need to be either just one such thing (in which case the self and the aggregates would be the same thing, totally identical) or there would need to be several truly existent things, totally separate from each other. Since neither of these is logically the case, then there is no such thing as true existence. Voidness is the absence of true existence – the absence of there being either one or many truly existent things.