i'm hardly a word nerd. but i do recall bits of a class discussion from like junior high english class.
driveways are paths that connected public ways (roads) to private buildings. named for what you did on them.. with the advent of the automobile and garages to put them in, they've become places people often park their cars.. they've just gotten a lot shorter since most houses no longer have acres of farm fields, barns and outbuildings, and what not surrounding them.
parkways are wide, and often landscaped, thoroughfares originally through, you guessed it.. parks. they don't necessarily always go through parks these days but the concept is generally still the same, unless a local government is misusing the term for naming a road. they are also not usually the main route, but rather the recreational or scenic route, between their end points.
both words predate the automobile.