The word degree has many meanings, but in academic terms, it refers to a certification awarded at the university level.
The B.A. degree (Bachelor of Arts), for example, is awarded upon completion of a four-year program of study requiring a specified minimum of credits.
An M.A. degree (Master of Arts) requires two or more years of study beyond the B.A. and carries with it the passing of certain examinations and, usually, the completion of a thesis or other research project.
The Ph.D. degree (Doctor of Philosophy) requires several more years of study, examinations, and research projects beyond the M.A.
In addition to the degrees awarded by four-year institutions of higher learning, community colleges offer the Associate Degree upon completion of two years of study beyond high school.
A diploma, on the other hand, is a document testifying to the completion of a course of study. Any graduate, whether of a university, a high school, or a six-week course in Spanish, will receive a diploma.
High schools issue diplomas and certificates of attendance, but they do not award degrees. To describe a person as having “a high school degree” is an error of fact as well as one of diction.