Graduate degrees are usually referred to Master degrees (MA, MS, MBA) or PhD. Professional degrees are graduate degrees in a specialized field such as Law (JD), Medicine (MD, DO), Dentistry (DDS), Veterinarian Medicine (DVM).
Some universities offer a larger diploma size for master degree or PhD but many will use the same size as the bachelor degree diploma. However, most universities issue larger diploma sizes for the professional degrees and the school's administrative office instead of the university's registrar's office handle matters related to the diploma.
Note that universities/schools sometimes change the diploma size. When ordering a diploma frame, it is imperative to provide either the exact dimension with margin measurement of the diploma, or the graduation year and degree type to ensure that the mat board opening will fit the diploma perfectly.