What's the difference between vaginal tears, lacerations and abrasions after childbirth?

Not much: They are all pretty much mean the same thing; sometimes abrasions are used to mean more of a very superficial tear.

Essentially the same: Vaginal lacerations are the same as vaginal tears. They are very common after delivering a baby. There are various classes based on how deep the tear is. Treatment is surgical repair immediately after delivery.