A subdomain is similar to a normal domain name, but requires a primary domain name. It is used to create sub pages for a website like forums.domain.com, support.domain.com and so on. Since subdomains uses your primary domain name, it is free of cost and you can create as many subdomains as you like for your website.
An addon domain is a new domain name which has nothing to do with other domain names. It is similar to creating new website using a new domain name with your existing account.