"고 나서", "ㄴ 후에" 나다, the base form of 나서, is used in -고 나다 form to mean "on completion of an action or event". 후 is a noun for "afterwards", similar to 뒤. So the two expressions are about the same in meaning. Both are widely used, but -고 나서 sounds more colloquial and better suited for successive actions, while -ㄴ 후에 is a bit more formal and can describe events further separated in time. E.g. 밥 먹고 나서 나가거라 - Eat before you go out. (natural everyday expression) E.g. 밥 먹은 후에 나가거라 - Eat before you go out. (same, but not as natural) 후에 can be used after a noun phrase too, as in 아버지의 사업 실패 후에 가계는 급히 기울었다 = 아버지의 사업이 실패하고 나서 ...