Parked domain is nothing but a domain which is working as main domain and distribute the same content of your main domain. It is a parallel domain. Both main domain and parked domain shares the same file in the same hosting.
Add-on domain: Add-on domain is nothing but a domain which has separate data base, files, content etc. they have separate entity for all the access. An addon domain is an additional domain that the system stores as a subdomain of your main site. Use addon domains to host additional domains on your account.
Login to your name cheap domain dashboard or login to your name cheap c-panel
Click on setting icon in near to addon domain
Three you see an option is called create an add on domain.
Enter the domain name and sub domain name (you can choose any name) also after entering domain name the sub domain name automatically will be created. Then click on add domain as shown in the figure.
In the same page, by clicking the domain name you will be redirected to file manager. There you can upload any file of which related to your domain. Also it functionally differs of the main domain.
To delete the add-on domain, => Login to your C panel and go to add on domain settings gear => then click on remove the domain
Also when you deleting the add-on domain, the file also will be stored in the same hosting and it should be deleted manually.