Markup and discount percentages are standard business arithmetic. Both can be used to express the same transaction, in different terms.
Markup, you buy at 100% and sell at (100% + markup). Discount, you buy at (100% - discount) and sell at 100%.
They're not equal, and it has to be clear which one you are using. For example, a 25% markup and a 20% discount represent the same ratio ( 125 / 100 vs. 100 / 80 ).
Usually, you use markup to figure your selling price vs. cost of goods sold, stating your markup as ( other costs + profit ) / cost of goods sold. It's also useful to use markup when analyzing a chain of distribution, since the arithmetic is easier than it is with discounts. Two entities each taking a 50% markup gives a (150% x 150% - 100% ) = 125% markup.
You use discounts in negotiating, buying and selling. If you're a retailer, you ask for a discount; if you're a distributor or wholesaler, you offer one. Thus Valve demands, and gets, a 30% discount on licenses they resell; and makes a 43% markup when they sell them.
Financial institutions have another, deliberately misleading, use of discount percentage, but that's even further off topic.