"Sites allowed on the account" means a separate websites hosted as a part of the service plan. In cPanel Shared Hosting account they usually work as add-on domains. "Domains supported (parked domains)" are just domains parked to account!
A parked domain is an additional domain that points to the main directory of your account (sort of like an alias). You can park unlimited domains at no cost on both the Basic and Business plans.
Or, if your hosting allows additional domains you can purchase additional domains and point them to the nameserver of your hosting. Makes for a cheap new website if all you are buying is the domain. I have 11 different domains under one hosting account right now.