What car?
Is the noise coming from front or rear?
The rust around the edge is normal, the clean face is from contact with the friction material of the pads.
The face of the discs should be almost polished in appearance and smooth to the touch (a few light grooves are ok but the important...
Is it grinding that you can feel through the steering wheel or pedal, or a higher pitched squeal? If it's the latter it may be a squeal indicator telling you that your pads are low. If it has gone metal to metal it'll be a set of pads and possibly discs depending on damage.