The snaffle rein (top rein) works mainly on the mouth piece with very very light poll & curb pressure. You main contact should always be with that rein.
The curb rein (bottom rein) works the shank, the curb and poll pressure. The more pressure you apply the more pressure there will be on the curb & poll. The poll pressure aids to the horse lowering its head & the curb does two things, stops the bit from rotating to far & through applying pressure guides the mouth to remain closed.