I think they aren’t quite the same: “buy 1 get 1 free” means that you only get a discount if you remove at least 2 units of inventory from the store. If I wanted to encourage people to clear out shelves in order to make space for new inventory (like an entirely new product or the same product but with more distant expiration dates), I might be inclined to use “buy 1 get 1 free” (or something like “buy 3 get 1 free”) rather than just reducing the base price: if someone only gets the discount if they help me clear the shelves it might make our incentives more aligned. A “buy 1 get 1 free” deal might also make it easier to reinterpret statistics: being able to say “we sold 100 units at a price of $2 for each unit (but there was a buy 1 get 1 free deal)” might be more useful than being able to say “we sold 100 units at a price of $1 for each unit”. Also, information about who took advantage of the deal and who didn’t might be interesting (based on what was bought at the same time or tracked with a “loyalty program”), but a constant discount doesn’t make that information available since it applies to everyone equally.