You are confused I think. In the context of vegetarianism, shell fish, fish, poultry, game and "meat" are ALL "meat": the flesh of any kind of animal is "meat".
In just about all other contexts (for example, religious, sections in a shop or recipe book, menus etc.) there are "significant" differences between these types of food. I can only speak for the UK but if you went to a fish and chip shop or a fish mongers and tried to purchase beef or pheasant you would fail. A butcher would not be expected to supply fish. Most people would not expect to be offered game pie or liver and onions in a seafood restaurant. Whilst you would find rabbit, pheasant, venison etc. in a shop selling game, you would be unlikely to find pork or halibut. You would not find, say, bacon and mackerel in the same section of a super market.
There are many people who, for religious reasons, will sometimes eat fish but will not eat other types of meat. So-called "pescatarians" will eat no meat except fish.
It would be silly if these distinctions, which are understood by everyone except (it seems) you, did not exist.