- 끝나다 (vi) = Something ends or terminates (on its own), as in "The movie ended" (영화가 끝났다).
- 끝내다 (vt) = You/They end something (needs an object), as in "The teacher ended the class" (선생님은 수업을 끝냈다).
* These can also be said in the long form 끝이 나다 and 끝을 내다 to mean the same thing with more detail.
For example, you can say things like:
- 아홉 시쯤에 일이 다 끝났다 = The work finished at arournd nine. (note 이)
- 아홉 시쯤에 일을 다 끝냈다 = We finished the work at around nine. (note 을)
(In the first one, 일 is the subject. In the second, the subject is "I" or "we" " which is omitted)
- 우리는 그때 끝났어 = We (i.e. our relationship) ended then.
- 우리는 그때 끝냈어 = We ended it then (끝내다's object, like 우리 관계를, is left out - it sounds better not naming the obvious thing).
끝나다 creates a sentence of S+V while 끝나다 makes S+V+O, but because Korean often drops the subject and/or object, the two forms can look very similar, as in the last example.