In the Irish language "Táim" is generally followed by something else (an action for example)... "I am going to..." or "I am looking for..." whereas "Is ... mé" is used in cases where you are discussing something more definite. "I am a man" or "I am a policewoman", that kind of thing...
Another way I learnt it was that:
"Táim" is used for when you are expressing something that will most likely change. E.g. "Ta me go maith" - "I am (doing) well."
But you use "Is" when expressing something that probably won't change. E.g. "Is Eireannach me" - "I am Irish".
Hope that helps.
I wrote "You and I are" that was wrong. If it was a answer to a question it might be, "we are" The only way it would be said in such a way would be like "who is going with us to the park."(to a group) and you spoke and said, I am and(look around)( or point to).....she is." There are other ways, but I agree it is strange in context.
There are two ways of expressing the English verb "to be": ta and is. The difference is somewhat similar to Spanish "ser" and "estar," if that helps. Google something like "irish ta versus is" and you'll find a good number of sites that will explain the difference clearly.
Going to give it my best guess here. When I say táim, I mean "I exist". I wouldn't use it to mean that "I am a man" or "I am a doctor" or whatever -- for that I would use "Is ... me". Same thing with tá sí/ is ... i. "Tá si" = "She is." (That is, "she exists"). "Is ... i" = "She is ..." (as in, "She is a woman ["Is bean i"]). I think this is how it works, but don't take my word as gospel.
'Tá' comes from the same proto-Indo-European root as English 'stand' and expresses a copula for "state", while 'Is' comes from the root that gave the English 'is' and respectively expresses an "essence". The difference between the two notions has already been explained, I just wanted to provide a hint how one may remember them more easily.
"Is" is used to show that the following two words are equal and are talking about the same person or thing. It cannot be used to mean I exist and she exists, nor to use adjectives to describe people or things. http://www.irishgaelictranslator.com/articles/grammar/ta-and-is-the-to-be-verbs/