Both mean "after doing X, then Y". 후에 attaches to noun or verb noun form. 고 나서 attaches directly to verb stem.
Tip: 고 나서 is slightly more colloquial. Both are very common in everyday speech.
Examples
| Korean | English |
|---|---|
| 밥을 먹은 후에 운동해요. | After eating, I exercise. |
| 숙제를 하고 나서 놀아요. | After doing homework, I play. |
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