Is there a difference between these two sentences?
Generally, 不 negates the word(s) right after it.
Therefore sentence 1 can be interpreted in two ways depending on the context:
Sentence 2 is simpler, 不 negates only 学习, so he is in the school, but doesn't study.
And you can add sentence 3: 他学习不在学院, which clearly indicates he does study elsewhere.
他不在学院学习。// He won't study in the school. It implies he will do something else in the school, e.g. play. And it can also imply that he is not the student in the school.
他在学院不学习。// The sentence implies a condition as if saying if he's in school he won't study. It also implies that the way to get him study is to make him somewhere else. E.g. 他在学院不学习, (在其他地方可能会学习). It can also be that the purpose he is in school is not for study but something else.
So, both sentences can be interpreted differently. We need context to understand the true meaning.
他不在学院学习。 This sentence needs a "tense" to clearly indicate the person's status - 他已不在学院学习了。 Also, I think 讀書 (study) is a better choice than 学习(learning).
他在学院不学习。 This sentence needs conjunction in between the phrases and a modifier before 不学习 to make it sounds complete - 他在学院但不好学习。
It is clear that the subjects following "不" are completely different, so the meanings of the sentences.