Those English words are synonyms for me. What is the difference? When do I use one or the other?
That will probably depend on what variety of English you use or in which English-speaking area you are - I suspect that the usage varies geographically and perhaps over time, too.
For example, I would have described myself, living in Britain, as a 'school pupil' but later as a 'university student'. Other people in other places and times may be 'school students'.
'Pupil' also has a sense being of 'disciple' or 'follower' of some teacher, so that might also be used for people who study under somebody else. In comparison, you might be a student of a subject such as psychology or Welsh.
Whatever the distinction is, where the English word is pupil/disciple, the Welsh equivalent is disgybl.