Classgrabber works because students busily add and drop classes throughout the registration and add/drop periods. When a student drops a class, it usually stays open for only a short period of time -- sometimes 15 seconds to a minute. Classgrabber sees the open seat and adds the class for you.
When you let the Registration Agent do your registration for you, it will automatically log in to the school's registration system at the right time, and start trying to get your classes. The Agent will notify you as it successfully gets your classes, or if it has an error trying to get them.