Obviously, the two terms come from the same Latin root. And in most cases the terms are interchangeable. (It’s similar to the difference between entry and entrance.)
What does one have to do to gain admission to this performance?
What does one have to do to gain admittance to this performance?
Most thesauruses (thesauri?) will probably indicate that the two words are completely interchangeable. However, I would disagree, at least from an American English perspective.
For the word-phrase admission tickets, it would sound awkward to use admittance. Same for the phrase ‘price of admission’.
Also, for confessions and personal statements, admission sounds far more natural and correct than admittance. "By his own admission, he didn’t leave work until late that night."
There may be other examples, but I can’t think of any right at the moment. Those are the two main caveats that I would try to remember.
-Tim
