Affiliate marketing is a performance based marketing. Where you get commission when someone purchased something from your recommendation or a link specifically designed so that you get commission.
Email marketing is essentially a part of affiliate marketing or you can say a promotion method. You build a relationship with your list of subscribers who join your email list to get more information or join your newsletter. And from time to time you send emails to your list which can be both purely information emails or promotion email and earn commissions when people click on the link inside the email and buy the product.