I think the official word (at least in the US) is "accredited" university for an official university, and "unaccredited" for an unofficial university. I think I've met a few people who've attended an unaccredited universities. There are a few legal differences between them, mainly on the university's end - like whether or not they can claim certain things as tax breaks. But they also matter on the students' end: not being able to have it "count" for jobs that have specific educational requirements, like your friend not being able to use it as a reference for being a teacher.

There's nothing about being unaccredited that necessarily makes it bad. A lot of them are things like seminaries or divinity colleges. They don't really need to be accredited, since they're already getting all of the tax stuff for being a nonprofit and a religious institution, and the graduates are only ever going to use the diploma to qualify for a position in the religious institution they're attached to. Some of them are as high-quality as accredited colleges. Some of them are real institutions that just haven't gotten accreditation yet because they're so new. But practically speaking, a lot of fraudulent unaccredited educational institutions are basically diploma mills. You pay them money, they say you're certified in something, even if you haven't taken any courses in the subject.