Translation:She is a college student and studies a lot.
As a native speaker, I'd say there's a big difference. Studying would refer to the act of studying, reading, and doing homework - you could do a lot of it and not learn much. Learning means actually understanding and retaining information, while studying is more of the attempt to do so.
In English "to teach" and "to study" are two different verbs, but in Russian the latter is the reflexive form of the former. "Учить" has other meaning as well, but here I'm talking about the "to teach somebody". By turning it into the reflexive "учиться" we get, broadly speaking, "to teach oneself" i.e. "to study".
Она студентка и много учится. Take the sentence and think about it as if you were hearing it. You would know that она is the only subject, so there would be no confusion.
Now, try this: Она студентка и она учится много. It's less clear if both она's are the same girl.
For your statement, you have to use a который clause. Который is an invaluable tool to continue a sentence while clearly refering back to the subject. Она студентка, которая учится много.
We have to accept the Russian sentence as it is, even if it sounds limping to non-Russian: the И is supposed to coordinate two verbs, but here the first one "есть" is implied. To GarettTree: what is the difference between который and какой, both being translated as "which" ?
It depends on the variety of English you speak and how precise you wish to be. In American English, student is a general term, whereas in the UK student up to high school may be pupils.
In Russian, студент / студентка can only be applied to the education you receive after you finish school, so "college student" or "university student" (or "undergrad") is a possible translation.