As a former member of a HS cheer (and colorguard) squad, I'll explain the differences between Pop Warner, All-Star and School squads.
All of these have their own federations: All-star cheerleading is a relatively young sport and does not have an official association that is in charge of events. Companies that run competitions include AmeriCheer, US Spirit, Universal Cheerleading Association (UCA), National Cheerleading Association (NCA), American Cheer Power, Cheerleaders of America (COA), World Spirit Federation (WSF), The competitions that take place at Disney World are usually Nationals. (Which my squad never had the luck of making it to....)
All-Star cheerleaders often cheer for whichever team they happen to belong to. So if there is a squad from "Indian Hills All-Stars" (Whose colors are Blue and Red) They would have a cheer something like this

This is a made up cheer squad....)
Go Blue (Audience says Blue) AND Red. Come on now BLUE and RED!
Their cheers will also have something to do with the name of their teams as well.
For some All-Star squads, you have to audition. For others, it's kind of like a Dance Team at a Dance School that competes against other dance teams from other dance schools. The parents help to defray costs for membership on the squad.
School (and college squads) require auditions. They cheer for their school, mascot and their school colors.
,
I consider cheerleaders cheerleaders as long as they are cheering for something. So, under my definition, all the types of squads that you spoke of in your post are Real Cheerleaders.
I hope this answers some of your question.