The answer is, of course, yes and no. Like so many words in English, "meat" has multiple meanings. Meat in its primary definition is "the flesh of an animal". Since fish are animals, fish is meat. However, this if more for biology. In the culinary world, meat is used primarily only for the meat of a mammal. Therefore a chef or proper grocery would separate "meat" into meat, fish and poultry. It really has nothing to do with Catholicism, but Catholics do use the culinary definition of meat meaning mammal meat when it comes to abstaining. From the dictionary:
2
: animal tissue considered especially as food:
a : flesh 2b; also : flesh of a mammal as opposed to fowl or fish
b : flesh 1a; specifically : flesh of domesticated animals
So if you want to speak correctly, if you are a vegetarian obtaining from meat, you would include all "flesh of animals". If you are at the grocery picking up some salmon to go with pasta, you wouldn't say you're there for meat; you're there for some fish.
