I have always called a light top with a full zipper to be a jacket, however the people I'm surrounded by insist on calling it a sweatshirt. I'm prepared to be wrong, just wondering if I'm the only one.
A hoodie (in some cases spelled hoody[1] and alternatively known as a hooded garment)[2] is a type of sweatshirt[1] with a hood that partially or fully covers the wearer's head or face.
Wikipedia says that the zipper can be a defining characteristic: