domain addon question

I am new to websites so bare with me.

I set up an addon domain but I'm confused, I thought it was suppose to be completely independent from my original site.

The URL is like this though. "www.addondomain.origionaldomain.com"

Is this how It's suppose to be? Instead of "www.addondomain.com"

Does the hosting service you use allow you to have unlimited domains or more than one domain? If it does, ask the techs, they'll give you fully detailed instructions (and tips on how to use cPanel better probably) on how to add a domain, probably way more information than what we'll give you since they own it. If you're using HostGator...they have live chat which will allow you to talk to a tech.

I'm allowed to have 5 addon domains.

What you ended up with is a sub domain actually.
And you're right, an addon domain is an independant domain and should be as www.addondomain.com.

Check back in your cpanel.