If the Fallout world were anything like our world. But it's not.
That said: things would get confusing for the general population. And the terminology scheme would get messed up same as it is in our own world. There are so many terms to choose from: assault rifles, battle rifles, marksman rifles, automatic rifles, submachine guns, light machine guns, carbines, etc, etc, etc.
With regards to the realism of the in-game naming scheme: you need to take into account the variation of the application of weapons terminology through history, and the many contemporary variations in terminology. A contemporary North American English terminology wouldn't necessarily work for anyone who's not from North America, and even many North Americans would disagree with any chosen terminology.
True. Hitler coined Sturmgewehr. Any word with "Sturm" in it was vastly popular in Nazi propaganda. This is also the reason why contemporary Germans often avoid the term.
Still, even Germans were and are confused between the applications of Sturmgewehr, Maschinengewehr, Maschinenpistole, Maschinenkarabiner for various weapons. Definitions vary.