Not that it matters at all and there is never a need to strictly hold yourself to a dietary rule. The term for a vegetarian that eats eggs and dairy is "Lacoto-ovo vegetarian"

I've been mistaken for a vegetarian a few times even though I'm not, and have never claimed to be. I don't eat pork (no, not religious reasons, just don't like it) so when I ask for no bacon, sausage, etc people automatically assume I'm a vegetarian. I don't quite know how they jump to that conclusion.

I've never been big on meats and these days there's loads to choose from which is non-meat. Given the option I'll choose plant based.