From what you say, it does sound like a catr fight.
We have an urban fox who lives on the canal bank behind our house, and he appears around seven every night because some people on the state feed him. He sits and waits at the bottom of their drive and after his tea, he has a wander around. There are loads of cats on the estate, but i have never heard any noise when the fox is around, which would be likely if he was trouble for them.
Cats are territorial, so an occasional scrap among neighbours is very common, I would immagine this is what you heard. They are usually more about noise and fury than injury, and eventually the pecking order is settled, so don't owrry too much about it.