떠나다 Means to leave, exit, bail, 출발하다 means to leave, depart, start off, start out, pull out.
Examples: 일찍 출발하다- To start early or make an early start.
다시 출발하다- Make a fresh start.
핸디캡 없이 출발하다- Start over or start from scratch.
이제 떠날 시간입니다- It's time to leave.
기차가 역을 떠났다- The train left the station.
아침 일찍 떠나다- Leave early in the morning.