I also have a 50 dollar coupon

On the other side of book keeping- if you sell an item for $10, if you receive two $5 bills- you now have a tax liability to report the sale as $10. If you sell an item for $10 and get one $5 coupon and one $5 bill- the sale can be reported as $5 for tax purposes depending on your book keeping. A coupon backed by the seller is self financed and there is no additional profit. Something like a manufacturer coupon is subsidized by the maker of the goods- so the seller is reimbursed all or some percentage- meaning you get $10 total for the sale still- but it’s $5/$5 and you can account that in different ways.

A manufacturer might instead offer an “incentive.” That is common in cars and appliances etc. that means that for every Washing machine you sell- the maker will pay you... say $500. So if the machine is normally $2000, you could still sell it at $2000 and make $2500- but if you discount it $50 more people may buy it and the total you earn may be more. Of course you can discount it $250 and hope for more sales while keeping the other $250 as well.

So where an incentive or rebates etc. are offered by the factory- instead of offering a “rebate sale” (depending on the laws of that land-) the store might instead self issue coupons for all or some of the rebate amount on the chosen item. Then the sale of the item can be reported at a lower amount and the rebate can be accounted separately from the sale of there is benefit to that for the retailer. Movies make extensive use of such accounting as do car dealers etc-

You see- it’s possible for tax purposes that a movie like Starwars or the Marvel films can have little or even $0 “net profit” or even be shown as a loss which can be used as a tax deduction for studios. Another reason? Payroll. Movies, cars, sales, executives etc. often get commission, “points,” bonuses etc. for sales or net profits and so on. By reducing the amount that hits the books as total sales or total profits- you can “tweak” the numbers so that even when performance is good- you don’t have to pay high bonuses or commissions. Anyone looking at such jobs should be mindful of this: the accounting office can control your commission to be whatever they want. There are few performance based pay plans where earnings are not capped to some range beyond which they will not be allowed in general.

Tl:dr- not a coupon. Paying money towards a purchase reduces the total you still owe the same as a coupon does- but HOW it does it and the specifics of how it works are not the same- and exploring math etc. you’ll see that there’s a difference. For example- on paper 1+1 and 2/2 are the same- but Having a kid and a second on the way is very different than having 2 kids and your spouse leaving you and getting custody of the second. Theory meets reality. But ultimately by definition of the word- money isn’t a coupon.