Undergraduate Brit checking in,
College usually refers to post-16 education, for example 6th form college. And institutions that provide pre-degree level qualifications.
College can also refer to an institution that provides degree level qualifications, and possibly following a US institution many people refer to Universities as college.
Universities proved degree level qualifications which can be. . .
Bachelors degree, if you’re studying for one of these, you are an undergraduate. This usually takes three years, but doesn’t usually follow the Major minor system, although some universities offer this. I’m studying Drama, and that’s it, nothing else at all. Joint Honours degrees are also offered, which is an equal balance of study between two subjects.
If you continue study after getting your bachelors, you become a post-grad student, and will usually be studying for a Masters degree, which is usually an additional year of study in a much narrower field of study than your undergraduate degree.
(Some under-grad degrees are MAsters, these are integrated four year courses, in which you never get a bachelors degree, but after four years have a masters)
From here you can continue study as a post-grad student to get a Phd. (Doctorship), this entitles you to be called Dr someone, but in my experience Dr. someone is usually only used for official correspondence.
To become a professor, you must enter academia and be promoted to this position by peers in your fields, this take years and years, and probably won’t happen until your in you 50’s/60’s.
There’s lots of other qualifications as well. But I hope that helps, and is fairly clear.