1. Pescatarian - no meat except for fish (which is meat, darnit!)
2. Semi-veg (or a 'flexatarian... I don't know where they come up with this)- someone who likes to eat vegetarian but is not adverse to eating meat.
3. Lacto-ovo veg - No meat/fish, but eat eggs and dairy (take off lacto for no dairy, take off ovo for no eggs)
4. Vegan - no meat, no eggs, no dairy, nothing processed with animal derivatives, and in my opinion, a LIFESTYLE, not a diet. If you are a vegan, great, but if you simply eat a vegan diet, I believe it's different.
And then there is a raw vegan (unprocessed vegan, nothing over a certain degree in F... I think 105 or something?)
Macrobiotic, also unprocessed vegan, but allows some fish. No sugar, nothing refined.