发生 (fā shēng) is the general, neutral verb for 'to happen, to occur' — used for events, accidents, and changes. 出 (chū) is more colloquial and often appears in fixed phrases like 出问题 (a problem arises) or 出事故 (an accident occurs). 爆发 (bào fā) specifically means a sudden, violent outbreak (war, volcano, anger) and is more formal.