Admission - Admittance

Can anyone explain the difference between these two words and give some example sentences. Thanks!

Admittance used to be applied mainly to a place: admittance to the cinema was restricted. I was not admitted because I came too late
Admission to a society or class: the admission of the new Fellows took place yesterday.
In general usage the boundaries of the two words are beginning to blur. Admittance/admission to the museum is free.

An admission is also an acknowledgement: I admit I was wrong. (I hope I’m not in this case…)