Addon Domains (cPanel => Addon Domains)
An Addon Domain is a domain name which points to its own folder within public_html and appears as a separate website from your primary domain.
This allows you to have two separate web sites on your account. You can have a dog.com and then a cat.com as an add-on domain. The cat.com would be a completely separate web site and visitors would not know that it is part of your dog.com account.
Alias (cPanel => Aliases)
An Alias is a domain name that points to your main web site on your account.
For example, if dog.com is your main web site, you can purchase the dog.net and assign it as a parked domain so that if a visitor were to type dog.net they would see the same web site as if they had typed dog.com.