Doesn't matter in the case of the Facebook app. I believe it uses location services to stay alive in the background regardless of turning background activity off.
It does a bit of both. I also turn off Facebook's ability to get location if it isn't active. Haven't had problems with battery use since doing that. I also don't use Facebook often, so YMMV. (Although interestingly, since getting my iPhone 7, it's never requested location access, so that's one reason why it doesn't hit my battery very hard)