Voucher (=call out, or tell) and coupon (=cutting) are different means to communicate marketing message. Both can be used for the same purpose, e.g. sales promotion.

Coincidently, both were made of paper. Voucher was used as a one-piece paper to be handed over to the recipient.

Coupon was a two-piece paper, to be cut, where a copy was given to the recipient while the other kept by the person.

Other means of communication are tickets, chips, coins, tokens, etc.