Hi, Andrea. They are pretty much the same. I thought about them after reading your question and every example sentence I looked up in my Korean dictionay to see if I could explain to you any differences between them means the same whether you would choose to use either one. ●일을 마치면(or 끝내면) 식당으로 와라. ●그는 면도를 끝낸 후(or 마친 후) 거품을 닦아냈다. ●방학을 끝내다(마치다). Hope this helps.

Although, 끝내다 and 마치다 both used interchangeably each other in daily life, there are some differences in usage. 끝내다 used for the work which is affected by intention or will 마치다 used for the work which is not affected by intention or will 끝내다 used for the work which can be stopped 마치다 used for the work which can not be stopped 끝내다 used for the work requires assertive efforts 마치다 used for the work requires adaptational patience 끝내다 used for negative works 마치다 used for positive works

둘다 비슷한 말이지만 끝내다는 '어떠한 일을 끝내다' 처럼 무언가를 완료한 상태를 말하고 마치다는 끝내다와 비슷하지만 어떤 과정을 마치다 또는 수업을 마치다 와 같이 쓰입니다. 하지만 수업이 끝났다로도 쓰일 수 있죠~ 결국 둘은 비슷합니다