It's true it can stand for both. The history is:
DVD originally stood for Digital Video Disc, but then, the big players wanted to offer DVD as a separate technology, not to be confused with "videos", so they changed the V to Versatile.
Similar to what Blockbuster does in their ads, they say "available on video and DVD" ... separating video from DVD, and offering it as a different technology, because most people associate "video" with poor quality VHS's.
In either case, the name is a little redundant.
Good luck.