I'll admit I haven't watched the episode of the clone wars show that featured the dark saber (or any of the series, for that matter) but from all the screenshots/pictures of it, it looks like some fancy black sword that happens to be glowing white, with a far more defined shape than a lightsaber. It does NOT look even remotely like a "simple" lightsaber with a black core. (wiki article says it was originally going to just be a regular vibrosword, but Lucas didn't want lightsabers to be able to be blocked by regular weapons that look like swords, so it was made special... 'course, Unless I'm missing something lightsabers are getting blocked by vibroswords all the time in TOR (and KOTOR, for that matter), as well as similar weapons in the books.
I do have to agree with many of the other posters. The black core lightsabers just look silly/out of place.
(P.S. In the clone war episode, does said darksaber every actually "extend"? or is it really just a black sword with a white glow outline?)
It is called a Darksaber.. Keyword Saber. Lightsaber keyword Saber. Dark vs Light. Yes it is a Jedi weapon it is a darksaber.. Did I repeat it enough for you to comprehend.. Thank You and you have yourself a great day.