I'm curious about terms that can be used to describe these people, or the qualifications themselves:
- College/university graduate
- Somebody with a "Master's" qualification
- Somebody with a "Doctorate" qualification
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A good general word for someone who has graduated from a school is alumnus. It has the added benefit that the same word is used in a number of languages and is easy to recognize.
A useful phrase in this context is also titulus academicus, an academic title. If you say ille magister est, it is unclear whether he is a teacher or a master. If you mean the latter, you can say titulum academicum magistri habet. This allows you to specify what you mean.
There are several ways you can translate "degree". In analogy to Italian, laurea is an option. Vicipaedia uses gradus academicus, which is a good choice. One option is to go with diploma (neuter!) and pair it with a suitable adjective.
You can translate "doctorate" as doctoratus and similarly magistratus for masters. The latter has an established meaning, but that should not interfere if the context is clear enough in context.