"Did you see the boy coming?" = when the boy was coming, did you see him?
"Did you see the boy who is coming?" = did you see the boy who can be identified as the same boy who is now coming (or will come in the future)?
Closer to the meaning of the first question, but still different, would be:
"Did you see the boy who was coming?" = did you see the specific boy who was coming (as opposed to some other boy)?