~ㄹ/을 때 is more general, and indicates something happening at the time of another event.  The coinciding time is short.

~(으)면서 is like one thing happening continuously while another thing is going on.  It implies the two things go on simultaneously for a while.

So you can say:

- 건물에 불이 났을 때 난 밖에 있었다 = I was outside when the fire broke out.  (-ㄹ 때 indicates a single point in time)

- 건물이 타면서 유리창들이 깨졌다 = The glasses shattered as the building burned (-면서 indicates some amount of time)

- 학교에 갈 때 비가 왔다 = It rained when I went to school.

- 나랑 동생은 학교에 가면서 장난을 한다 = My little brother and I play around while going to school.

~(으)면서 is sometimes shortened to ~(으)며, as in 학교에 가며..., although ~(으)면서 sounds more detailed.

I think '면서' is similar to 'and'

Maybe "involve what 'and' means" will be more expression

In addition to '~때' makes verb into noun, but '면서' can't

Those are same santance in terms of meaning

But 면서 means more 'something happens in same time'

~때 means more 'time concept'. i think it is perpectly same as 'When'

I have some korean knowledge, but i can't english well . I REALLY hope you can understand it. If i have grammertical problem, can you me a favor?