공짜... free , 무료 (無料)...free, no cost. 공짜 is natively Korean and is used almost exclusively in casual settings. 무료 is hanja-based and can be used in both casual and also formal settings. Otherwise, they're virtually identical. Free is free. P.S)) 무료 (無料)...*Be careful to confuse this with 무료하다 (無聊) which means to be boring or dull. It most certainly does not mean to "to be free". Good luck!! :D