Advaita Vedanta can be called a mystical path, a spirituality, science of reality, or a combination of both (which I prefer). It can be called nonduality or ‘Monism’ (preferably the first): monism because it takes reality as being One (“without a second”). Nonduality because – though reality is one in essence or ultimately – it presents itself as apparently two: purusha-prakriti, Self- not self, sat-asat, subject-object, Atman-brahman. That apparent dichotomy, as stated, is reducible to the one reality which can be called variously ‘pure consciousness’, ‘the absolute’, ‘sat-chit-ananda’ (being-consciousness-bliss)… the unnamable. Words – language – is secondary, needed to express what is in itself inexpressible. What is inexpressible can be/is a (self)realization of ‘what is’ (anubhava) arrived at by intuition and (Vedantic) reasoning.
From he above it can be seen that Berkeleyan idealism is quite different. One similarity is that both systems deny the existence of an external world, but the idealism of Berkeley retains the validity or reality of minds and ideas. There is no problem with having God as the final ‘arbiter’ or Witness, since this notion or reality is (ontologically) equivalent to ‘the Self’ or pure Consciousness. Towards the end of his life Berkeley came to a position akin to pantheism*, not quite different from Advaita which, as stated, is a mystical, experiential Way (knowing-being), but properly it is not not pantheism. In Advaita the apparent multiplicity of forms/objects is denied – they are just names and forms (nama-rupa) , but in the end (with full comprehension) they are not other than the way Consciousness or the Self manifests Itself, thus ultimately not different from It.
* His last work, ‘Siris’ c.f. Colin M. Turbayne’s “Berkeley’s Two Concepts of Mind”
c.f. Greg Goode on Non-duality (Western types of).
Unanimous Tradition / Tradición Unánime 