certificate = a document containing a certified statement especially as to the truth of something; specifically :a document certifying that one has fulfilled the requirements of and may practice in a field.Typically not a college degree.
Diploma = document bearing record of graduation from or of a degree conferred by an educational institution,typically.This specifically mean that piece of document.
degree = a university degree (associate,bachelor's,master's or doctor's degree) from a post secondary education instutition