Step-by-step explanation:
You'd have to check your reference material (text, on-line tutor) for the "official" definitions of each.
In my experience, both are a reduction in price. Whether the reduction is called a markdown or a discount may depend on the reason for it.
A discount may be part of a general pricing structure or plan: a customer may obtain a discount for paying in cash, paying within a particular time period, as part of a promotion or benefit (new-customer or employee discount, for example). Goods that are "on sale" may be advertised as having a particular "discount."
A markdown may be a reduction in price because goods are damaged, out-of-date (unfashionable, or near/beyond their expiration date), or for the purpose of reducing unwanted inventory. A discount on items that "must go," or a reduction in price to better match market conditions, may be called a markdown—a reduction in the asking price of real estate, for example.