The only time two cats are really fighting or are getting ready to fight is when they let out growls at each other. Usually when cats swat at each other without any growling, it is their way of playing, although sometimes it is one cat's way of establishing dominance over the other. However, my older cat Tabitha will occasionally hiss at the younger cat Phoebe when she just does not feel like playing. Phoebe always understands and goes about her merry way.