מבחן - is the literal translation of test. בחינה - Is more like an exam. It's plural form could also be used to talk about tests and exams in general, but then you'd say בחינות (exams in plural). בוחן - quiz The same way that they're interchanged a lot in English, they can be switched around in Hebrew.

As far as it concern exams, I think בחינה and מבחן are synonyms. Maybe each one has some other meanings, but in this *aspect - there is no difference. * For example: בחינה has also a meaning of an aspect..