Some common types or synonyms of shirts and tops:
T-shirt
polo shirt — a shirt with collar but only a partial vertical opening with buttons
shirt or dress shirt — a shirt with collar and full vertical opening with buttons
tank top — a sleeveless T-shirt
wife beater — a tank top worn as an outer layer
blouse — ladies shirt — the term is also used for some men's military uniform shirts.
nightshirt — for sleeping
sweater, sweatshirt — with or without hood
rugby shirt — typically a rugged long-sleeved polo shirt
Hawaiian shirt — a colourful short-sleeve dress shirt
guayabera — an embroidered dress shirt with four pockets
golf shirt — a polo shirt
baseball shirt — usually distinguished by a three quarters sleeve
first shirt — the "shirt" is a nick-name for a First Sergeant