-(으)면서 has two meanings.
The first meaning is ‘during/while’ which two actions happen at the same time. For example,
밥을 먹으면서 TV를 봤어요. I watch TV while I was eating.
음악을 들으면서 공부를 해요. I study while I am listen to music.
요리를 하면서 많이 먹어요. I eat a lot during cooking.
인터넷을 하면서 길을 걸으면 안 돼요. You should not walk while you are using the internet.
운전하면서 핸드폰을 보지 마세요. 정말 위험해요.Do not look at your phone while you are driving. It is dangerous.
제 아내는 자면서 이야기를 해요. My wife talks while she is sleeping.
그 사람이 울면서 말했어요. That person talked while he was crying.
The second meaning is ‘yet, though’ which two opposite actions happen at the same time. For example,
돈이 없으면서 돈이 있는 것처럼 행동합니다. Someone acts like he/she has money even though he/she doesn’t have money.
아무것도 모르면서 다 아는 것처럼 말하지 마세요. Do not say like you know everything, yet you don’t know anything.
요리는 안 하면서 먹기만 해요. Someone just eats although he/she doesn’t cook.
-(으)며 also has two meanings.
The first meaning is the same as -(으)면서 which is ‘while/during’ but a little formal. And the second meaning is the same as -고 which is ‘and’. For example,
음악을 들으며 운동을 하고 있습니다. (=들으면서) Someone is working out while listening to music.
그림을 그리며 노래를 했습니다. (=그리면서) Someone sang songs while someone was drawing.
그 사람은 피아노를 치며 노래를 불렀다. (=치면서) That person sang songs while he was playing piano.
서울은 한국의 수도이며 경제의 중심입니다. (=수도이고) Seoul is the capital of South Korea and the center for finance.
그 사람은 피아노도 잘 치고 기타도 잘 치며 노래도 잘합니다. (=치고) That person plays piano, plays guitar and sings songs very well.
제 조카는 공부도 잘하고 춤도 잘 추며 운동도 잘합니다. (=추고) My niece is good at studying, dancing, sports.
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