I understand that imitation is repetition within a polyphonic texture...so my understanding is that for example, when the trumpet part repeats the string part at 0:21 in this piece by Handel (), this is repetition rather than imitation. But the grey area for me is, if a part repeats in another voice within a polyphonic texture, maybe a bar or more after the first part has finished...is this imitation or do the 2 parts need to overlap?
'Imitation' is a very broad term for a very broad musical concept. Imagine a composition where a melodic or rhythmic element DIDN'T often echo something already heard?
Let's start from the Wikipedia opinion - "the repetition of a melody in a polyphonic texture shortly after its first appearance in a different voice."
OK, that excludes rhythmic imitation, and avoids the question of how exact the copy should be - imitation need not be literal. But it'll do as a basis.
Your question hinges on how short is 'shortly'. An overlap obviously meets the requirement! Simple re-use of a melody several pages later obviously doesn't. I'd suggest: 'Imitation is when a repetition directly follows the initial statement. Nothing of import should intervene. But it need not actually overlap.'
There is a special name 'Stretto' for a series of overlapping imitations where the entries DO overlap, 'piling up' on each other. Look at the first musical examples on this page: