Sub domain
Lets say your domain is mysite.com.
You install a Message Board and put in in a directory called mysite.com/board/.
You can turn the directory board into a sub-domain by adding it as a sub-domain from your Control Panel.
Now you can access your Message board as either mysite.com/board OR board.mysite.com
This costs you nothing and is free.
Parked Domain
You have two domains mysite.com and my-other-site.com.
mysite.com is the domain of your website and you want to add my- other-site.com.
You want them both to go to the same place. In other words, when someone types either www.mysite.com or www.my-other-site.com they will go to the same page(s) on your website.
In order to have additional parked domains you need to purchase the additional domain(s).
Add-On Domains
You have two domains mysite.com and my-other-site.com.
You want the two domains to be totally separate/independent websites.
In order to have additional parked domains you need to purchase the additional domain(s).
source : http://webnet77.com