In the airline industry, they will give you a '(travel) voucher' for a specific sum, even if it's only for partial value. It is a form of refund or concession after the sale. 'Discount' would be a price reduction prior to purchase, though we don't see that as much in that industry, as the prices change constantly anyway.

In general, ‘voucher’ is a more serious word often suggesting legal rights, government involvement, and higher value. ‘Coupons’ are less formal - referring to a marketing discount.

In the US, a coupon is usually something that will give you a discount whereas a voucher is something that you exchange for the full value of something...i.e. if you have a voucher for something, you would exchange the voucher and receive something without needing to pay any money. A 'rebate' is something where after you buy something for full price, you can receive back a portion of the cost if you send the rebate back to the company/manufacturer that sold it.