Associative vs Groupoid - What's the difference?

As an adjective associative

is pertaining to, resulting from, or characterised by association; capable of associating; tending to associate or unite.

(algebra) a magma: a set with a total binary operation.

(en adjective)

Pertaining to, resulting from, or characterised by association; capable of associating; tending to associate or unite.

such that, for any operands

a, b, c

(a * b) * c = a * (b * c)

(computing) addressable by a key more complex than an integer index

Awk's associative arrays may be indexed by strings.

Associative memories were once given considerable attention.

* antiassociative

(en noun)

(algebra) A magma: a set with a total binary operation.

(algebra, and, category theory) A set with a partial binary operation that is associative and has inverses and identities.

A groupoid is a category in which every morphism is an isomorphism.

* (wikipedia "groupoid")