Disclaimer: I'm not a native speaker, but I did go to high school in Korea for a while. In my experience, 중간고사 and 기말고사 are the official college or high school exams at the 1st semester and year-end, respectively. I took 중간고사 in the summer and 기말고사 was in December, so they roughly correspond to US exam periods. I haven't heard of 기말시험 but it sounds equivalent to 기말고사, but perhaps not as formal.