Direct sales is when you sell your product or services direct/straight to the consumer. The consumer doesn't have to come to your physical store. You can deliver the product via a distributor or a sales rep. For a digital product, you just send the customer to a download page.
Affiliate marketing is when you allow other people to sell your product or service for a commission, the affiliate does all the marketing and promotion and when people buy your product through their link/phone number you give them a commission.
The difference is that, with direct selling you have to do all the promotion, advertising and get customers then you also have to pay the sales rep or distributor to deliver the product. If it's a digital product then you don't need anyone to deliver the product, the buyer just goes to a download page to get the product.
With affiliate marketing, the affiliate does all the marketing, promotion, get customers and advertising. You can still do the promotions yourself to maximize profits, that way you don't have to pay anyone a commission. If it's a physical product you still have to pay for delivery and pay the affiliate marketer.
The biggest advantage of using an affiliate marketer is that most of them already have a list of buyers.