Aside from bovines and pigs, a common restriction is
Vegetarianism - no animal flesh
It has numerous variations, including semi-vegetarianism or
Flexitarianism: eating only some kinds of animal flesh.
Pollotarianism - only the flesh of poultry birds: chicken, turkey, quail, duck, goose, etc. (Galloanserae). I can't find anything on whether other birds are OK, like ostrich and pigeon.
Phylogeny:
- Palaeognathae: ostrich, ...
- Neognathae:
- Galloanserae: chicken, turkey, duck, goose, ...
- Neoaves: pigeon, ...
Pescetarianism - only seafood: fish, shrimp, clam, ...
Pesce-pollotarianism - only seafood and poultry
I can't find anything on the allowability of meat of amphibians and reptiles: frog, turtle, lizard, snake, alligator, crocodile. Let's see where they are phylogenetically.
Tetrapoda:
- Lissamphibia: frog, salamander, ...
- Amniota:
- Synapsida: Mammalia
- Sauropsida:
- Testudines: turtles
- Squamata: lizards, snakes
- Archosauria, crocodilians, dinosaurs: birds
So a pesce-pollotarian might find amphibian and reptile meat OK, and a pescetarian also, since amphibians and reptiles are like fish in being cold-blooded.
Turning to pescetarianism, it encompasses the flesh of all non-tetrapod animals, like fish, crustaceans, bivalves, cephalopods, ... a potential problem is land invertebrates like insects and escargot (snail).