The Sturmgewehr 44(“Storm Rifle”) (StG44) was THE rifle that created the “Assault Rifle” class.
Early engagements were fought with rifles designed around parameters that did not match up with the realities of World War 2.
If the Allies wanted to overtake a fixed German position, the Garands(.30-06) and BAR (.30-06) were most effective at long ranges that the rifle was designed for, the M3 and Thompson fired .45 ACP which was most effective in CQB, you had to gather the appropriate equipment operators and pray to God that “not too many” of your riflemen were dropped or you would lose effective suppressing fire and that your SMG assaulters could actually take the position because they were the only ones with the right equipment to effectively do so. Add in the fact that your smgs and battle rifles were chambered for different calibers, and you had significant supply logistic problems.
The Germans had the same problems and they only got worse as the Western Front was opened up and supplies had to be selectively shuttled around 3 different fronts (French, Italian, Eastern) The Kar98k, Gewehr 43 and MG42 fired 7.92 Mauser, the Mkb42 fired 7.92 Kurtz (not interchangeable with Mauser), the MP40 fired 9mm Parabellum.
As the war went on and war analysis was performed, it came to be understood that the accuracy and range of the Kar98k was wasted on any soldier but a trained sniper and its low fire rate was woefully inadequate for standard infantry engagements at the ranges they actually occurred. The StG-44 was implemented to be able to perform the duties of a battle rifle(range;fire base), a carbine(maneuverability), and a submachine gun(assault). It had selective fire so that the operator could switch between semi-automatic for ammo preservation and automatic for close quarter combat spraying. It fired the intermediate, 7.92 Kurtz cartridge to maintain the range of a Battle Rifle needed for WW2 engagements, the recoil characteristics of an SMG for accuracy during full automatic fire, and the ergonomics of a carbine. With the StG 44, each squad operator can perform in each required assault role (suppression, fire base, maneuvering fire, storm)
We call the class the “Assault Rifle” specifically because of the StG-44 and the functional properties that were designed into it. All modern rifles in the class are its direct descendants and any rifle which is not directly descended from it with its desired goals designed into it are not Assault Rifles.