【Acceptance】 and 【acceptation】 have both at one time or another carried the meanings: the act or fact of accepting or the state of being accepted. Present usage, however, restricts their denotations.
【Acceptance】 only is used to denote the act of accepting.
a blind 【acceptance】 of authority —Inge
Or the state of one who accepts something, especially something inevitable or inescapable.
all settled back into a sad sort of 【acceptance】 of the situation —Delano1)
Both 【acceptance】 and 【acceptation】 may be used to denote the state of being accepted or especially of being approved or believed.
metrical forms are conventional, and therefore rest . . . on 【acceptance】 —Lowes
【Acceptation】 tends, however, to confine itself to denoting the sense in which a word or expression is generally received.
not... a cultivated man in the ordinary 【acceptation】 of the words — Eliot
