When you want to buy or sell something on the stock exchange, you give an order that defines the transaction you want to make. This instruction, the order, is transmitted to the exchange. When your order is matched on the exchange, that is, when your buy order matches someone else's sell order, the trade is executed. At that point, the buy or sell is complete. In short, an order is your request to the exchange and a trade is the realization of that request.