Judging by how many active players there are, there is probably thousands of competitions going on at the same time.

As was already said, any Cup competition starts off with 128 random teams and they are selected from all levels.
As regards the Champions League, you qualify by finishing in the top 4 of your domestic league. In each CL competition they start with 32 teams split into 8 groups of 4. Then top 2 progress to the knock-out rounds. In this competition, all entered teams are of equal level (or at least until the higher levels of the game).