There really isn't a need for two terms, vegetarian and vegan. Vegetarian can only mean that one doesn't eat anything but vegetable matter, which includes fruits, nuts, legumes... even grass if you fancy grass. Logically it can't mean fish. Or shellfish. Or eggs, or dairy, or even insects.

I have stopped calling myself vegan. There isn't a need to distinguish between those who eat no animals in any form and those who eat some animals or some parts of some animals, because if they do, they are logically not vegetarian.

I suspect the seeming need for a term that emphasized the non-eating of any animal matter was the result of people who still ate animal matter, wanting to seem as though they didn't. That offended those who really were vegetarians, so they created a name for themselves, leaving the word 'vegetarian' for those who still ate eggs, fish, dairy etc. That's too illogical to me, so I have gone back to just saying I'm vegetarian, and if asked if I eat eggs (for example) I just answer that eggs aren't vegetable.