"T-Shirt" bras are a catch-all term for bras that can be worn under a t-shirt: completely seamless cups for a smooth appearance.

"Padded" refers to any bra that has moulded foam cups to prevent show-through (not necessarily push-up)

"Spacer" is an ultra-light foam (due to the 'spacer' of spongey material between fabric layers) that makes these padded bras more flexible, breathable and better-fitting!