The most basic shape is a straight edge. These have no curve in the sweep. Any chisel with some curvature to it is considered a gouge. These tools can have a gentle curve that goes all the way up the neck of the blade.
You can also get carving chisels with a gouge only at the end. These tools are spoon-shaped and called front bend gouges. Gouges can even have a concave bend or a backbend.
Furthermore, you can get a gouge that is wide at the sweep and gradually narrows until the tang. Some people call these “spades,” perhaps because they look like shovels. You may also see these referred to as “fishtail” tools.
Gouges are categorized by numbers from one to 11. You will see these written as “#1, #2, #3,” etc. #1 is another way to categorize a flat chisel. On the other end of the spectrum, #11 is almost a perfect semi-circle. The other gouges exist along the spectrum.