"초등학교", "중학교", "고등학교", "대학교" "교" (learning..?) "숙직실", "사무실", "경비실" "실" (rooms.. or place?) 교 + 실 => "교실" normaly. "교실" means high school or middle school or element school teaching room. but, "강의실" is more general. 강의 = "Lecture" + 실 강의실.

교실 = in school up to high school 강의실 university and college.