안 & 지 않다 mean the exact same thing, except one is seen as more formal and one is more casual. The mistake Korean learners often make is..

아니다 = to not be, 없다 = not exist, not have, 안 & 지 않다 = not, don’t, 못 & 지 못하다 = can’t do, ~(으)ㄹ 수 없다 = can't, 지 마세요 = don't do it