The term "assault rifle" refers to rifles firing a mid-size rather than full-size cartridge, having a large capacity magazine of at least 30 rounds and the capacity to fire in full auto.
They're called "assault rifles" because the idea behind them was that infantry in the assault could provide their own "covering fire". A measure of support that was traditionally provided by stationary machine guns or another formation that was stationary and in a firing position.
This originated in WWI with weapons such as the Pederson Device, Fedorov rifle etc. It reached "perfection" in WWII with the Kurz 7.92 cartridge and the MP44 and similar German "assault rifles". They called them "Storm(ing) Rifles": "Sturm Gewehr".
Anything else is simply a semi-automatic rifle, no matter how black it is, how many folding stocks, pistol grips, picatinny rails, flashlights, lasers or other do-dads you stick on it.
Some people feel cooler if they tell the gaping onlookers that they own "assault rifles"

"I'm big, I'm bad, I own ASSAULT RIFLES".

Sorry kids, it's not an "assault rifle" unless it meets the definition.