Actually, vegans refrain from eating both chicken and fish.  There are several classifications of vegetarians and vegans are among the strictest.  They don't eat any meat or meat products including dairy and eggs.  There are even some vegans who omit honey from their diet as they consider it to be an animal product.

Now as mentioned before there are several types of vegetarians, including some that do eat chicken and/or fish.  They are called pescatarians, pollo-vegetarians and flexitarians.  Pescatarians, one of the more moderate types of vegetarians, omit all animal flesh from their diet with the exception of fish.  Pollo-vegetarians refrain from eating red meat, but do eat poultry.  Meanwhile, flexitarians are a classification of vegetarians who continue to consume meat, but merely reduce their intake of it.

With the increase of people adopting a vegan diet, there are bound to be some that may refer to themselves as vegans, but be observed consuming fish or chicken.  However, realize that this is probably due to a lack of education about the differences in vegetarian classifications.  Alternatively, they may be in the process of transitioning from a pescatarian or pollo-vegetarian diet to a vegan diet.  For most, converting to veganism is a gradual process that often begins on the vegetarian track.  Thus, its not such a bad thing that they refer to themselves as vegan.  It just means that they are on the path toward realizing that goal.

So if you're thinking about becoming a vegan, but can't yet shake the meat addiction, take your time.  Making the transition gradually will ensure that you also make the transition permanently.  After all, given the benefits of a vegan diet, it is most probable that once you become vegan you will remain vegan.