These ludicrously long legumes aren't just hulked-out green beans. They're in the same family, of course, but they're closer to cowpeas. Which are similar to black-eyed peas. It's a family vine!
Here on the West Coast we tend to call them, easily enough, long beans. Occasionally we even say “Chinese long beans.” In other, less Pacific Rim–influenced areas of the country, they are known variously as yardlong beans, asparagus beans or snake beans.
Tastewise, there is no difference between purple and green, though the green are far more common here. In a surprise twist, they aren't particularly good for steaming or boiling: they'll almost immediately go mushy. Instead, prepare them with oil in a skillet or a wok. They're an excellent stir-fry ingredient. Or, fry them first and then add them to whatever you've got on simmer. You'll probably chop them up first, of course.