The word “ranger” does not come from “range” …
Actually, it does. However, more in the context of ranging over ground, not ranged combat.
ranger (n.)
late 14c., “gamekeeper,” agent noun from range (v.)). Attested from 1660s in sense of “man (often mounted) who polices an area.” The elite U.S. combat unit is attested from 1942 (organized 1941).