I think the term “assault rifle” was originally German, but many countries experimented with semi-automatic or automatic rifles, and got the idea that a smaller rifle with a caliber smaller than what the bolt-action rifles had might be practical. But yeah, anything the left doesn’t like, from guns to freedom of speech to you owning your own car, is “Nazi.”
Stg 44 stands for SturmGewehr literally “storm rifle”...what Storm Troops would use while storming forward so they would not have to have machine gun support and would not have to stop to reload.
Other languages translated “Storm Rifle” as “Assault Rifle”.