Sweatshirts are double-layered pullovers, typically non-woven. Sweaters are single-layer pullovers, typically knit. Jackets have buttons or zippers. Hoodies have hoods and are made of fabric (e.g. raincoats are not hoodies).

You can have hoodies that are also sweatshirts, or hoodies that are also jackets.

This garment pictured in your post is a jacket. It is also a hoodie. It is neither a sweatshirt nor a sweater.

This is just my interpretation of the situation. I don’t know of any formal classification system for outerwear.