What is the difference between a dwarf spheroidal galaxy and a globular cluster?

The main difference is if it is gravitationally bound to another galaxy or not.

A globullar cluster is a group of old stars inside a galaxy. It is not independent.

A galaxy is a group of stars, and a dwarf sheroidal galaxy is a group of (mainly) old stars, gravitationally bound in itself, but not bound inside a larger body (even when it can be orbiting a local group center of mass).

If Segue 1 is orbiting around Milky Way's center, it is a globullar cluster. If it is orbiting with Milky way about Local Group's center near Andromeda, then it is a dwarf spheroidal galaxy.