Semi-vegetarianism

Semi-vegetarianism means eating seafood or poultry, or both, but no red meat. People who eat red meat on rare occasion are "flexitarians". Real or semi-vegetarians, though, usually resent "flexitarian", looking down on this term and calling it cheating. 
A pescetarian is a person who eats fish, shrimp and seafood. They do not eat poultry.
A "pollotarian" is a person who eats chicken. They do not eat red meat, seafood or fish.
"Pollo-pescetarians" eat seafood, shrimp and poultry but no red meat.
People who have semi-vegetarian diets are usually doing so for health reasons, including avoiding heart disease, diabetes and strokes.