The manufacturer is going to call the rifle anything they want. Typically, it's the manufacturer's name and some other sort of designation.
I use AR-15 to refer to a whole class of rifles that have the same operating system and are descended from the orignal AR-15 series of rifles designed by Eugene Stoner and manufactured by Colt.
If you want something that is the same as the current military M4 (less the burst feature and/or full auto feature) you will have to do some looking around. For example, the rifling, barrel length and barrel profile are going to vary. Personally, unless you are in the military and just want to practice with something that is close as possible to what you might use in combat, I wouldn't worry about that. Just find some shorter barreled, collapsing stock rifle of that type that you like. Close enough.