Jaws did have a lot of blood...and even a lost limb...but it was still PG. The token slasher flick really came about with the Friday The 13th flicks, Halloween sequels, Nightmares, and tons of other bad non-sequel movies in the 80s, so yeah, that is pretty much when that genre took off. Stuff just got nastier and nastier and became scary in terms of BOO scary and shit jumping out at you or grossing you out, but not scary scary like the ones mentioned. I guess maybe they became more about physicality than mentality. The good scary shit gets in your head and stays in there.
You're right about the Paranormal Activity movies. I mean, they're all kind of overplayed at this point, but if you've never seen one before, they're a pretty good ghost story (except the theater ending to the first one...the alternate ending on DVD is actually better).