The chief difference between starch and glycogen is that glycogen consists of long glucose polymer chains with a significant number of branch points, usually at every 8 to 12 glucose residue, while starch consists of both amylose and amypectin, typically with fewer branch points. Starch molecules are also considerably larger than glycogen and may even be visible by microscope.
Glycogen is produced by animals and starch by plants; both store energy and feature a spiraling structure. In addition to having generally fewer branch points, the number of branch points in a starch molecule can vary wildly. A single plant typically produces some starch molecules with branch points and some that will contain none at all.