I can’t swim here.
I am not able to swim here.
I am unable to swim here.
I think these three sentences seem exactly simlilar.
Is there any difference?
I can't swim here – this does not necessarily mean you do not know how to, it can also be because you are bound by some rules etc (you may be banned from the pool, say).
I am not able to swim here – this necessarily means that you do not know how to. You are allowed to but you can’t because you don’t have the skill/confidence etc.
I am unable to swim here is exactly same as the last one, just I feel a tad bit more polite.