Hi Janie!
There are several types of vegetarians: the most typical, perhaps, are lacto-ovo vegetarians, who eat dairy products and eggs in addition to plant foods. There are also lacto-vegetarians (plants plus dairy) and ovo-vegetarians (plants plus eggs).
Back somewhere in the early 80's, when a lot of people were avoiding "red meat," some author (I read the guys book, but don't remember his name)invented the terms "pollo-vegetarian" to refer to those who ate ALMOST a vegetarian diet, but with the addition of poultry, and "pesco-vegetarian" for those who ate ALMOST a vegetarian diet, but with the addition of fish and seafood. Unfortunately, this has lead to some confusion, and there are now many people who refer to these diets as "vegetarian," though they really aren't. Of course, people can eat whatever diet they choose, but those who eat chicken and/or fish and call themselves 'vegetarian' are a source of consternation for those of us who wish to keep the real meaning of words.
As Michele stated, a vegan not only avoids all animal products in food, but also in other areas wherever possible (in practice, being a total 'vegan' may be impossible, but I see it as a continuous goal to strive for). Some people use the term 'vegan' to refer to diet only, while others prefer to use the term 'total vegetarian' or "dietary vegan' for those who eat vegan, but may still wear leather or wool, etc.
FYI: The term "vegan" was invented about 70 years ago by a British man (who just recently died) who was involved in a British vegetarian society, but wanted to go further. He formed an off-shoot organization, and called those who abstained from all animal products "vegans" (pronounced "VEE gn"...I had no idea how it was pronounced when I started reading about it!) by taking the beginning and end (the "extremes") of the word 'vegetarian').