The rust band can occur even with a properly functioning caliper.

What happens is that the edge of the rotor rusts a little, turns into sand paper and wears the pad away at a faster rate than smooth steel. Now that the pad no longer wipes the surface, the rust continues to grow wearing more of the pad. With this much rust, it is a definite safety inspection fail.

Check the operation of the caliper pistons as part of a proper brake replacement.

With this kind of rust, driving the car normally won't show any odd behavior, only hard braking will net early front brake lockup, you may also get pull if the rust is significantly different from side to side.

The second type of rotor rust would be scattered islands of rust sometimes in the shape of the pad outline. This is usually caused by poor rotor quality but can occur on good rotors when metallic pads are used.