안녕하세요. I'd like to ask whether there's any difference in usage between these two verbs that, according to my few weeks of studying, mean the same thing. Is there any difference in saying, e.g., 가지 못해요 and 갈 수 없어요?
What an excellent question! There are differences in usage but it's hard to put it as a rule.
For example, 그는 공부를 못해요. means his academic performance is poor, while 그는 공부를 할 수 없어요. means because of his health, financial situation, family matters, or just simply loud noise from outside or whatever the reason might be, something prevents him from studying.
Koreans frequently substitute 안하다 with 못하다.
Teacher: 숙제 다 했어?
Student: 아뇨, 못 했어요.
Teacher:왜 못 했어?
My explanation only covers just a small part of this subject. I'll add some more if I can think of any.