If your vehicle is showing continuous scraping noise from wheels while driving that stops when braking, here are the most likely causes and the parts you'll need to fix each one.
Anti-rattle clips and pad support springs keep the brake pads stable and slightly retracted. If they are missing or installed incorrectly during a recent brake job, the pad will loosely vibrate and scrape against the rotor while driving, but goes completely silent when clamped tightly during braking.
The brake caliper needs to slide freely on its pins to release the pads after you let off the pedal. Lack of lubrication or torn boots cause the pins to seize, making the pad drag constantly against the rotor. Braking applies hydraulic pressure that masks the light scraping noise.
Many brake pads feature a small metal tab designed to scrape the rotor to warn you when pad life is critically low. While this often squeals during braking, it can also cause a continuous light scrape while driving that changes pitch or stops entirely when the brakes are firmly applied.
The thin metal backing plate behind the brake rotor is easily bent during tire changes, suspension work, or by road debris. It will scrape the rotor continuously, but the slight flex in the steering knuckle and rotor during braking can sometimes pull it just far enough away to temporarily stop the noise.
A failing wheel bearing allows the wheel hub and brake rotor to wobble slightly (lateral runout) while driving, causing the rotor to rhythmically scrape against the stationary brake pads. Applying the brakes clamps the rotor flat against the pads, temporarily stabilizing the wobble and stopping the noise.