Addon Domains: Hosting another site, within 1 shared hosting account. The new account will not receive access to a control panel just for that site. Data for the site will be stored in a directory specified by the user, but still within their directory.
Example: You own business.com and purchased a shared hosting account for it. You now have business2.com and want to host it. You go to business.com's control panel, make this an addon domain, and create a folder business2 at the root of your account's directory. (/home/business/business2; /home/business is the highest you can go; to put things in perspective, /home/business/public_html would be the files for your current site that are viewable by the internet)
Business2.com now has its own website seperate from business.com's content.
Parked Domains: You have business.com, and now purchase business.net, and want it to just display the content from business.com. You go to your control panel, click on parked domains, follow the form and submit business.net to the form. Now, when a user goes to business.net, they will see the same content as business.com.
In both cases, it goes without saying that you have to change the nameservers for the respective domain. Hopefully this was clear, but if it wasn't, let me know, and I'll clarify whatever doesn't make sense.