A subdomain is a second website, with its own unique content, but there is no new domain name. Instead, you use an existing domain name and change the www to another name. The subdomain name looks like forums.yourdomain.com, help.yourdomain.com, help2.yourdomain.com (assuming you already host yourdomain.com).
An addon domain is a second website, with its own unique content. This type does require you to register the new domain name before you can host it. So, if you want to host www.otherdomain.com, this is the solution. You need to configure the domain with necessary A records before adding an addon domain.
A parked domain is NOT a unique website. Instead, it is a masked forward to the primary domain name of your cPanel account, much like a website alias. Parked domains are commonly used when you need a place to park a domain you do not have a website for, when you have more than one domain that should lead to your primary domain, or when you have common misspellings of your domain name that you have registered.