Yes. I’ve actually got a small scar from getting nailed in the face when I was training. Usually, abrasions occur in hand to hand in places where the bones are close to the skin. The head is a prime example. This isn’t incredibly common in training, you need to be hit with a substantial amount of force, but in actual fights, it’s a lot more common.
There’s actually an abstract level where bruising is, effectively, the same thing. Bruises are just sub-dermal hemorrhaging, so, somewhere down there, your tissue tore, and now it’s bleeding.
As far as I know, it’s extremely rare for the blood loss to be significant, but it’s still small cuts and scrapes.
On top of that, there are a lot of ways the skin can be torn in a fight. Forensics splits this between lacerations, abrasions and contusions. Contusions are your normal bruises, though, there can be tearing of the skin at a surface level. Abrasions are where the skin’s been torn at a surface level, either by a direct impact, or by being scrapped across something, this can result in bleeding, but it doesn’t always, if you’ve ever scratched yourself raw, that’s a, mild, abrasion. Finally, lacerations, are where the skin is sheared against something, tearing it. Lacerations always result in bleeding.
(If you’re wondering why I know this, it’s because I keep a forensics primer next to me, whenever I’m working.)