Assault rifle is a term that is pretty well understood to mean a rifle with selct fire capability and firing an intermediate cartridge between an full power mmilitary cartridge and a pistol round.
As another poster noted, Hitler had given express orders that no new rifles were to be developed, but based on German research post WWI, the High Coomand saw a role for an intermediate cartridge that would operate effectively out to 300 yards or so to replace the SMG (really, a 50-100 yard weapon). The weapon was initially released as the MP43, and MP44 before becoming the 'assault rifle' StG44. There is some debate about whether the StG was originally classed as an MP to conceal a new rifle or because that is where it fit in the High Commands thinging (A superior SMG). Both Russia and Germany were huge users of the SMK, whereas the US, with it's 'rifleman' mentality considered the Garand the premier infantry weapon (althoyg issuing plenty of carbines and SMGs).
It should be remembered that the focus of the German infactry squad wa=s the machinegun (MG34 and MG43) and the other members of the squad were basically there to protect the machinegunners who were expected to handle the serious killing.
The US was certainly no pioneer in the assasult rifle, and in fact actively opposed any adoption of that type of weapon post WWII. All of the Allies except the US heavily favored producing something akin to the StG44 after the was. FNs FAL was originally chambered in the german 7.92x33mm at the insistence of the British, and Allied weapon development focused on and intermediate round (e.g. the British 280).
With the establishment of NATO, the decision was made to standardize on a rifle round, and the US pretty much rammed the 308 down the throat of the other members, with the understanding that the other members would select the common rifle.
The other members of NATO chose the FAL, at which point the US decided to go it's own way and adopt the M14 - a 'product improved' M1 Garand.
The whole stody is quite interesting - particularly the influene of a single man - Col Rene Studler - on the US adoption of the M14 and the repudiation of the whole assasult rifle concept. See "The Great Rifle Controversy" by Ezell.
and not so different a comparison from the STG44 "assault rifle" and the AR-15 that most folks call an "assault rifle"
