I've always been fascinated by these two words, as they seem to have the exact opposite meaning as expected. Is it because of the etymology? Or perhaps the meanings were switched at some point in time?
"The first parkways in America were developed in the 19th Century by Frederick Law Olmsted as segregated roads for pedestrians, bicyclists, equestrians, and carriages." They had "large landscaped central medians" and "often act as the approach to a large city park." Only later was the term extended. (Wikipedia)
Merriam Webster defines "parkway" as "a broad landscaped thoroughfare."
The verb to "park" originally meant
"To put strips of lawn down the centre or along the side of (a street, the main streets of a city)." (OED)
So a Parkway was a "way," or thoroughfare, that was "parked," or landscaped.
"a private road giving access from a public way to a building on abutting grounds." 1871. (M-W)
"Also, a private carriageway for a motor vehicle alongside, in front of, or leading to a house, garage, or other building; a drive." (OED).
So a driveway originally was a path that you drove on. Many older houses in the US still have such a driveway - you know, the circular kind that you actually have to drive on to get to the front door (see http://www.sawdays.co.uk/search/images/335/bbb1759a.jpg ) Only in modern times, when everyone owned a car, even in cities, and needed a place to store it, did the driveway become a place to "park your car."