신경을 쓰다 / 신경쓰다 = concern oneself with something. Mind something. (신경 = nerve) 애를 쓰다 / 애쓰다 = expend a great effort / exert oneself for some purpose. (애 = old word for guts) 신경쓰다 is very much like "to mind" or "to be bothered by" something tricky or annoying. 애쓰다 implies working very hard (physically or otherwise) to get something done. Examples: - 저 사람은 항상 저렇게 말하니까 심한 말 해도 신경쓰지 마 = He always talks like that, so don't be annoyed even if he says something bad. - 이번에 이사하는 데 친구가 짐을 나르느라고 애썼다 = My friend worked his butt off carrying all the stuff during this move.