Vegans

Vegans eat only foods of plant origin, no foods of animal origin; that means, no eggs, dairy products, or honey. Soyfoods, legumes, nuts and seitan form the protein building blocks, and are rounded out by grains, fruits, and vegetables.

Lacto-Vegetarians
Ovo-Vegetarians
Lacto-Ovo Vegetarians

Lacto-ovo vegetarians eat as above with the addition of dairy products (lacto) and/or eggs (ovo). This is the style of eating most often meant in America when people refer to "vegetarian." Lacto-ovo food choices, in other words, do contain some foods of animal origin, but no foods composed of the animal's actual flesh, or products thereof (for instance, if rice was cooked in chicken stock, it would not be acceptable to your typical lacto-ovo vegetarian).

Pesce-Vegetarians (sometimes called Pescetarians)
 

In addition to the foods above, pesce-vegetarians eat fish. (Most vegans and lacto-ovo vegetarians do not, by the way, consider those who eat fish "real" vegetarians --- you see why definitions can create divisions between people?)

"Vegetarian Sympathizers"

Folks who do eat meat, fish, and chicken --- but perhaps much less than they once did, and perhaps more carefully (they may choose organically raised meats). They lean somewhat towards a low- or no-meat way in their thinking. Frequently Sympathizers and Pesces are on the continuum towards a lacto-ovo or vegan way of eating.