Most squirrel hunting is for gray and fox squirrels.

Gray squirrel
The gray squirrel is the most common, living in hardwood and mixed forests in both rural and suburban country.
Fox squirrel
The fox squirrel is the largest, often found in open woods and farm country. Some public lands limit fox squirrel harvest.
Other squirrels
Black squirrels are a color phase of grays and fox squirrels. Red squirrels are small squirrels of northern and mountain forests.