If they don't make a serious attempt to hospitalise you or worse it's not really a fight: it's a scuffle at most. A fight is a full blown situation where people that aren't going to back down and are willing to use violence and are in the process of doing so and don't stop until they are forced to.

If someone throws a punch and the other guy blocks it and pushes him over and that ends it, it's a scuffle; there was never any serious intent to do harm it was just one guy trying to assert his dominance over another and failing. If the guy gets up and there's an exchange of blows or wrestling with the clear intention that one guy isn't going to be walking away from this then it's a fight.

If a mugger comes up to you and you give him a smack or a shove and he decides he doesn't want to bother then it's a scuffle. If he decides that actually he's going to go for it then it's a fight.

If you walk away from it unhurt, it probably wasn't a fight. You should have at least cuts and bruises, a black eye, all the usual injuries that go with fighting.