By LAWRENCE FELLOWS
These words are similar, but not synonymous. Admittance refers to gaining entry to a place, while admission may refer to a right or privilege of entering. Thus, you may gain admittance to the Lotos Club as a guest, but not admission as a member.
Admission may also be used figuratively in, say, the admission of hearsay as evidence. And that may lead to a hasty admission of guilt. In neither case would admittance be correct.