As mentioned AR stands for Armalite, The original mfg.
The term assault rifle originated with the German Sturmgewehr 44 (StG44)https://en.wikipedia.org/wiki/StG_44
In German it means Storm Rifle, But I guess in English it translate to Assault
It was a select fire weapon single/auto.
They label the AR15 as an "assault rifle" even if it's a semi auto variant.
Of course labels are powerful right? we all know that's why they label everything they want to ban as "assault", they even call things assault clips and assault pistols these days to demonize things in the public mind to make passing a ban easier.
About air rifles, I never had anything all that powerful my self, all the ones I had was in .177, But they make 22 and I think even larger air rifles and I know at least some of the 22's can actually reach in to powder arms territory.
I think they're pretty expensive though I know airguns can go up into the 1k's.
My stuff was always off the shelf crossman & daisy.. the really good stuff you won't find in a department store.
I read somewhere that (I think it was the french) had a air rifle division.
back in the day when everyone was using muzzle loaders the guys with the airrifles was BAMF's
With a fire rate 10x that of those with muzzle loaders, and with the added bonus no smoke generated.. old black powder produces a lot of smoke.
I don't what particular air guns they used or how powerful they was but apparently enough to kill.