A coupon is a printed piece of paper, which allows you to buy a product with less money than ours, or get it for free.

witness

A voucher is a ticket or a piece of paper that can be used to pay for something instead of money.

(more inclined to vouchers)

Cash coupons and gift certificates are actually casual.

There is also a saying that the government or units mostly use coupons to distribute benefits to employees, while businesses use coupons to distribute more.

North Americans seem to say more about coupons.