What is the difference between a graduate degree and masters degree?

There's no difference. A master's degree *is* a graduate degree. A graduate degree is a broad term encompassing all degrees earned after a bachelor's degree, including master's degrees, doctoral degrees (Ph.D., Ed.D., etc.), and professional degrees (M.B.A., J.D., M.D., etc.). So, a master's degree is a *type* of graduate degree.