Many people get the wrong impression on having vegan and vegetarian diets. I met a few cases of this before on one of my websites where this particular person claims to be a vegan himself yet showing photos to the public eating eggs, dairy products and alike. Yes, you read them right, these foods are not allowed for the vegans.
Probably the main and most appropriate way of distinguishing the two is that vegetarian is the diet category while vegan just falls under it as a sub-category. If you are going to read stuffs about vegetarian diets, you would have probably notice terms such as "ovo-lacto vegetarian," and "semi-vegetarian" and "vegan". These are the under cards of a vegetarian diet.
While general vegetarians do not consume animal meat, this does not prevent them from consuming animal products such as milk and cheeses. However, the different sub categories ease in differences between each. Vegetarian is a blanket term used to describe a person who does not consume meat, poultry, fish, or seafood.
The term semi-vegetarian is usually used to describe someone who is a vegetarian who consumes dairy products, eggs, chicken, and fish, but does not consume other animal flesh.
Ovo-lacto vegetarians are vegetarians who do not consume meat, poultry, fish, and seafood, but do consume eggs and milk. This is the largest group of vegetarians.
Ovo-vegetarian is a term used to describe someone who would be a vegan if they did not consume eggs. Lacto-vegetarian is a term used to describe someone who would be a vegan if they did not consume milk.
Vegan is the strictest sub-category of vegetarians. Vegans do not consume any animal products or by-products. Some go as far as not even consuming honey and yeast. Others do not wear any clothing made from animal products.