How the concurrent and parallel threads are managed?

So I have a doubt of how are those are managed.

I know that if we've a single-core system the threads will be using the CPU time that the OS give them, but...

What happend in multi-core systems ? are they taken a thread each core? What happen if we create more threads than core? will they be executed concurrently?

Is this managed in the same way independently of the library (OpenMP, pthread, Thread...)?