개발하다 = to develop. 낙후된 지역을 개발하다 = develop underdeveloped regions.
발달하다 = to be in a developed or advanced state. 강원도는 관광 산업이 발달했다 = The Gangwon province has a well developed tourism industry.
개발하다 is used in all tenses, whereas 발달하다 is most often used in the past tense (발달했다) or indicating a completed state (발달해/발달되어 있다) to indicated a developed state.