Well, there is "pescetarian." That's a sub-category of vegetarian, where you can eat fish. (edited since prior post explained it)
I would advise against trying to fit yourself into certain labels, though. For example, I am currently a lacto-ovo vegetarian. But I only use that term to conveniently explain to others. I eat eggs and cheese (which makes me lacto-ovo). But lacto-ovo people can also drink milk. But I don't drink milk anymore and instead drink soy milk.
So in essence, I see this as a personal growth journey instead of a race to being the "all-mighty" vegan (that's my goal though
). Congratulations on even beginning this journey! It is a fun and rewarding one. I wish you and your fiancee the best and most importantly, enjoy your new meals and experiences!