Is there any subtle difference between "to study" and "to learn"?

I think we can generally divide them like this, although the separation may not always be so clear.

To study is the action, (from the dictionary) "the devotion of time and attention to acquiring knowledge on an academic subject", so the activity itself.

To learn is the result of that action, or as you can see in the Dictionary again, "gain or acquire knowledge of or skill in (something) by study, experience, or being taught".

Well, you can study without learning, but you can't often learn without studying, at least in academic subjects.

Saying "I studied English" means you took classes in English. It does not necessarily mean you learned anything. Saying "I learned how to tie a clove hitch" means you actually acquired a useful skill.