A parked domain is an additional domain that points to main directory of your account / primary domain. You can park an unlimited number of domains at no additional cost. A parked domain will resolve to your primary domain name. For example, let's say your primary is abc.com and you park xyz.com. In the address bar if you type xyz.com it will resolve to abc.com (i.e., show content from abc.com) but in the address bar you will see xyz.com.
An add-on domain allows you to run a separate web site within your primary domain hosting account. When you create an add-on domain, it makes a folder in your public_html folder and you upload the site content into that folder. So essentially you are running 2 separate sites, separate content, off one account. For example, let's say your primary is abc.com and you create add-on domain, xyz.com. The add-on domain is pointed to the xyz folder under public_html. In the address bar of your web browser, if you type xyz.com it will resolve to / display the content in the xyz folder and in the address bar you will see xyz.com. You can create separate email accounts for each domain name regardless if it is a parked or add-on domain.
NOTE: Using parked domain names can cause a negative effect for search engine optimization / search engine ranking purposes. Because the URL will be the same for both sites, Google (and possibly other search engines) will likely consider this duplicate content. Google will penalize or ban one or both sites if this is found.