I'd think of "God" as a more conditional perception of what lays outside of the veil of general Monotheism (being a transcendent thing in which all life is subject to) both within mystical traditions of Monotheism (Judaism and Islam especially) and within HInduism there is this lifting of the veil of sorts, of the mind being the source or ourselves being finite perception of this universal play. The Brahman + Atman realization is the thing that seems to vary a lot between Dharmic schools but this general notion is not too indifferent to the aforementioned mysticism in other religions, I believe it's a very substantial thing.
But then, the words "God" and "Brahman" respectively, do seem to impose certain limitations philosophically - both, in themselves, being (if properly actualized) forms of realizations about existence as a whole.