Yea for sure you are correct on the I factor. However the Hindu concept has Atman(Self) which is sanskrit, and The Buddhists have Anatman, with is (Non-Self). For the Buddhism I study it generally okay for me to have the Sanskrit connection. I feel these two ideas are explained very differently, as Buddhism itself is a response to Hindu traditions, but I feel Hindus still talk about the Allness of the soul and its connection to the universe. I Buddhism it seems more like a non-issue and is explained as Emptiness, as in everything is the same (All) and our conceptions of Labling are the Empty discriptions because of dependant origonation, where everything is only perceived as a thing because of something else in relation to it. The non-issueness come into play because of the 'we are going to die, lets just get to the core of living this illusionary existence and what we are, knowing words are just feeble discriptive terms so we can talk about it." I feel for a broad broad usage, this peace or mindfullness would be a God of sorts, in the Verb tense of Ideal Living, those are my words.
The Hindu "I", is explained as a part of an Intageable God that we can know but not attribute Ultimatly, with words. However we are able to get deeply intouch with our own piece and this leads to seeing that in All. So this to me means like realizing that you aren't really you and that seems like a disolving into an emptiness of its own.
On this point I feel that is where the over lap is. Disolving our preconceptions of "Is-ness" Buddhism really cuts to the aesetic core of knowing the Highest of the Highnesses, Hindu or otherwise, and seeking not to become attached to that words and concepts we have about that Deep level of Living. Hinduism allows space for that understanding of Oneness as well as the Ulitmate goal of understanding, but scripturally speaking its more deffinative in it language, even though its taught in Upanishad like language that God is constantly being described in UnKnowable Knowables, which is alittle close to says this IS something vs trying to say something about a thing by NOT saying what it IS.
I think that Zen as a branch of Buddhism could be interchanged in this post, but its fair to say they aren't in Sanskrit although the ideas generally are the same. Granted there are alot of ways different branches get to that same point.
Blah, sorry for the long wind

But I just got my talk on about this, I really like to see the crossover in a cultures religion. You can know alot about history socially by looking at the problems movements tried to solve. Much like the protestant revalution in Europe from the 16th century onward. But comparing this movement to that movement is a whole other post, so I'm jamming on the breaks for now.
PeaceLoveSageTree