【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

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