There are a few different words in use, depending on how exact you wish to be. If you’re going for maximum exactitude, good luck! There are so many terms for varying stages and forms of vegetarianism that I personally know of no one who understands half.
The most common type of vegetarianism is of course lacto-ovo-vegetarianism, which is vegetarians who also consume dairy products and eggs. The word vegetarian is usually synonymous with lacto-ovo-vegetarian, except in specialised contexts.
If you eat fish, but no other kinds of meat, you are a pescetarian or pescatarian (the former is the historically and etymologically more correct spelling, but the latter has the advantage of showing more clearly that the ‹sc› sequence should be pronounced as /sk/). This is a relatively common word that will be understood by most.
If you eat poultry, but no other kinds of meat, you are pollotarian, though this is not a very common word and many will not know it.
If you eat both poultry and fish, but no other kinds of meat, you are a pollo-pescetarian (or pollo-pescatarian), which is a very rare word that I’m quite sure nearly no one will know.
If you eat poultry, fish, and bacon, but no other type of meat … then you’re just a picky omnivore, I think. I have never seen any word for (or even notional acknowledgment of) such a combination of diet choices.
A very useful term that covers all three highlighted words above is flexitarian, which is basically someone who’s somewhere between being an omnivore and a vegetarian. It can also refer to someone who’s generally a (full-on) vegetarian, but sometimes eats meat (possibly also including red meat), either as occasional one-offs, or as a change in their diet for shorter periods of time.
For some more useful information, see also the Wikipedia article on semi-vegetarianism and the links in the References section there. Don’t go in too deep, though, or you’ll get lost very quickly!