A subdomain name points to a subfolder of the primary domain. For instance, cats.pets.com would point to a subfolder such as /cats under the primary domain of pets.com. Its content is separate from the main site so it can act like a separate site though usually it will have some relevance to the main site as you can see above.
A subdomain can also be used on our system to redirect to somewhere else and create a shorter way to get there. For instance, mymail.mydomain.com could be redirected to http://mydomain.com/webmail/horde/ to get to webmail easier and force the use of the Horde webmail client. Unlimited subdomains come with each hosting account.
A parked domain is an additional domain that points to the main directory of your account. A parked domain will resolve to your primary domain name. Say your primary is domain1.com and you park domain2.com. In the address bar if you type domain2.com it will resolve to domain1.com but in the address bar you will see domain2.com. This is a parked domain.
An add on domain allows you to run a separate web site to your primary domain. 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.