Great question! I’m a native English speaker and I’m afraid I don’t have a great answer for you. They mean the same thing, but there are nuances that would make one sound better in a sentence than the other. For example the person that organizes a Conference is sometimes called the “Conference Convenor”, but we would never say “Conference Assembler”.

I’m more likely to convene a meeting than assemble it. But when we meet, I am more likely to say we have assembled than to say we have convened (but both are correct).

I am studying Japanese right now and I can empathize with learners of English. The subtleties of a language can be frustrating.

Hope this helps!

Thank you very much!