The difference between periodic and perpetual inventory is that perpetual inventory system records the cost of goods sold at the time of each sale. However, a periodic inventory system records the cost of goods sold at the end of the period. So, perpetual is every time, and periodic once at the end of every period. As for the difference between purchase discount and sales discount is that a purchase discount is usually from a store getting a discount from a manufacture for buying bulk. Whereas a sales discount is the store giving a discount to a customer. So, purchase discount is for the retailers, and sales discount is for the customers.