[globular-toast]

You have this the wrong way around. Associative array is the abstraction you are talking about. Hash maps are a specific implementation of that abstraction. You could also define hash map as an abstraction which has the same interface as associative array but with more strict performance characteristics. But either way it's wrong because bash is neither implemented as a hash map nor has the performance characteristics of a hash map.

For reference the main implementations of associative array are alists/plists (linear time), balanced binary trees, b-trees (logarithmic time) and hash maps (amortised constant time).