The interesting dichotomy comes from the use of the word "park" to mean a place to put something, and by extension a place for people to go to; and the verb "park" meaning the act of placing something somewhere.

The driveway is so called because it is the "way" to get to the "drive" (i.e. road.)

The parkway is so called because it is the way to get to a "park".  (Parkways were orginally intended as a means for people to get to parklands, and even to this day many parkways exclude commercial vehicles so as not to impede cars from getting to the parks.  Such was the publics insistence back then of the importance of these now, of overlooked jewels of an earlier time.  

But I digress.

There are several occurences of odd dichotomies in English.  For example, a person who rides a motorcycle is refered to as a biker, while a person who rides a bicycle is refered to as a cycliist.  The only reason I can think of for this one is that the terms arose without regard to each other.

Here's my favorite, created by the dual definitions of the term "permit".   This was a sign I actually saw while traveling on the Long Island Expressway in an area where the road was narrowed on account of construction:

The sign read:  "Permitted loads not permitted."  I sent that one to English chonicler extrodinaire, Richard Lederer, and he wrote back with gratitude for the nugget which he promised to air in some upcomming edition.  

You have to love a language that would allow that to make sense, n'est-ce pas?

I wonder if the sign painter had a wry smile on his face when he wrote that one.  (Or perhpas a rye smile, or for that matter, a Rye smile.  They all work.)