right, but a cardigan is a type of sweater, no?
that's why I'm thinking (let's just keep it American, and menswear) that a sweater is a catch-all for any knit top for men (excluding jerseys and knit polos). types of sweaters including crewneck, vneck, turtleneck, cardigan, sweater-vest, even hooded, etc.. can be any type or combination of wools, cotton, linen, etc.
and that sweatshirt implies that it's woven. these come in crewneck and hooded forms that I know of. hooded can be zippered as well.
These are just guesses but it's how it works in my head.