Since manufacturers took asbestos out of pads, they are almost as hard as discs. Consequently, as pads wear down, they also wear the disks/drums.
As the pad/shoe surface is smaller than the disk/drum on which it presses, you eventually get a lip forming - shiny disk with a rusty lip. New pads may be a fraction larger than the old ones or might not be seated in quite the same spot as the old ones so this will cause the constant grinding when you brake.
Had this on the wife's old Astra. In the end I whipped the disks off & attacked the lips with an angle grinder - solved the problem.
Harder to fix on drums but there are companies who will skim drums for a price.
Took it back to the garage a few times (whilst still under warranty (bought 2nd hand at 3y/o)) & told the above story about hardness of pads/disks. The mechs reckoned they change the disks at the third pad change.
There are certain companies who will replace pads free for the lifetime of the car (as long as you own it) - probably sting you for new disks though.