Sometimes there is no difference. Sometimes there is! Examples: I've got to catch up on all this work. I've got to catch up with all this work. Either way, I'm on catch-up! Oh dear! All that work! But with people it's only catch up with. I've got to catch up with my friend (he's ahead of me, walking faster). And we also use it to say 'see you later sometime' as in 'I'll catch up with you next week maybe.' or 'catch up with you later at the cinema.' I have work to catch up on now so catch up with you later, ok?

on后面经常跟事情，工作 with跟人