(불)타다 = intransitive "burn". 건물이 불탔다 (A building burnt). (불)태우다 = transitive "burn". 쓰레기를 태웠다 (I burnt the rubbish). (불)타오르다 = 불타다 + -아/어 오르다 (rise in intensity/scale) = to rage in flames. 건물 전체가 불타올랐다 (The whole building was engulfed in flames). These appear as a pattern with some verbs. - 자다 (vi, to sleep), 재우다 (vt, to put someone to sleep); 깨다(vi - wake up), 깨우다(vt - wake someone up). - 날다(to fly), 날아오르다 (to take flight); 솟다 (to rise/soar), 솟아 오르다 (to soar high); 뜨다 (to float), 떠 오르다 (to float up).

불타다 and 불타오르다 are similar they mean burn but 불태우다 it’s means you burn something