degree is a higher standard - if you imagine a mdular course, where by each module gets a certain amount of points for passing, you need less points to get a diploma than a degree
While I agree with Bednobs that a degree often represents a higher level of achievement than a diploma, it's not always the case. Some diplomas are 'degree equivalents'.
The strict difference is that a diploma is solely a qualification. A degree is admittance into a class of membership of a university. (There are some religious groups which don't allow their members to hold any memberships other than of the religious group. Members of those groups have to petition their universities to 'cancel' their degrees, because they count as memberships. They don't have to 'cancel' any diplomas they may hold).