Both are the same in meaning, but "사용(使用)하다(=to use)", which came from Hanja, is often used in written or more formal situations while "쓰다(=to use)", which is the native Korean word is commonly used in spoken like most native Korean words do. As you know there are lots of verbs came from Hanja or Japanese in Korean, and in most cases they are used in written. For example, to eat - 먹다, 식사(食事)하다 to add - 더하다, 추가(追加)하다 to pass(an exam) - 붙다, 합격(合格)하다 to achieve - 이루다, 성취(成就))하다 to embrace - 안다, 포옹(抱擁)하다 to forget - 잊다, 망각(忘却)하다 to overcome - 이겨내다, 극복(克服)하다 to take (time) - 걸리다, 소요(所要)되다 to produce - 만들다, 생산(生産)하다 to recover - 낫다, 회복((回復)하다 \^o^/

identical, but 쓰다 can be used to "write", "bitter" etc.