Those tags serve the same distinct needs as the varied D&D edition tags do — they reflect different varieties and versions of the game and its attributed setting. I'm not a fan of the nwod tag, as it's not official terminology, but here's what's intended.
storyteller-system is for the mechanics of the classic World of Darkness games. (1991-2004; 2011–)
storytelling-system is for the mechanics of the new World of Darkness games. (2005–)
world-of-darkness was intended to reflect elements of the setting of the games, but now has become a useful marker for the whole White Wolf WoD category, like dungeons-and-dragons is.
I can see a need for distinct settings tags for the old and new settings; I'd be interested to see what suggestions come up.
Edited: The comment thread causes me to suggest the following: