Inverts...Invertebrates are defined as, "anything without a vertebral column. This in effect includes all animals apart from the sub-phylum Vertebrata. Familiar examples of invertebrates include insects, worms, clams, crabs, octopus, snails, and starfish. Taxonomically speaking, "invertebrate" is no more than a term of convenience. The vast majority of animal species are invertebrates, since only about 3% of animal species include a vertebral column in their anatomy."
So your clean up crew "typically" is filled with invertebrates. Snails, crabs, worms of various sorts, and microscopic creatures like copepods, and arthropods. (Sorry about the spelling. I am an Engineer, not a Biologist)
I don't think its possible to have a true FOWLR without any traces of invertebrates (because there will always be those microscopic critters. That being said, I know that many people who have invert eating fish tend not to add snails and crabs to their tanks. They invest in "Giant arm snails" and a good filter.
And I "think" the term "Reef tank" is defined by the presence of corals. But I could be wrong on that front.
Happy Studying and good luck with you future tank