A suppressor traps a lot of the gasses which follow the bullet, in an unsuppressed rifle they exit the muzzle like a rocket engine and continue to drive the rifle back after the bullet has left the muzzle. A suppressor traps these gasses along with the bang and releases them slowly so thus you do get a reduction in recoil as there is less thrust being generated by the gasses.
It makes more of a difference in an overbore calibre as there is a lot more gas being pushed out of a narrow bore.
A brake uses this gas and reverses the thrust, thus dramatically reducing the felt recoil.
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