Here is the answer to that age old question....
 
By definition a driveway is really a private road that connects to the public street system. Today, these 'roads' are usually short, but the name sticks. We park our cars on them because, after having 'driven' the 'way' to the private house, we would obviously have to stop when we arrived.
 
We drive on parkways because the 'park' of parkway is not the same word as 'park' meaning to stop. A parkway is defined as broad road usually marked with scenery and a landscaped island. Scenery? Landscaping? Sounds a lot like a 'park', as in the recreation space. Thus we drive on parkways because they are glorified ('park' like) road (Latin 'via' = road, and 'via' is also related to the word 'way', hence a 'parkway' literally a 'park-like road'). Hope this helps.