generally a single video connector is output only, but some can automatically detect which way the signal is flowing and capture as well off the same port. You need to check your graphics card details - if it's marked up as VIVO (Video In Video Out) then it will capture.
So the answer is, probably not.
And yes a capture card is different to a video/gfx card. Video/gfx cards generally only handle outputs from the pc to monitors and tvs. (unless marked VIVO). Capture cards only handle inputs and outputs to vcrs etc.