|Allow us to simplify these terms for you:
Subdomain is a part of the main domain name but can run another website with unique content. For example, you have a domain name : abcxyz123.com running a website.
Add-on domain is a unique domain that needs to be registered separately and has it own unique content. Changes in your nameservers are required for hosting the domain. In simple terms, its another website with emails running on a Multi domain hosting plan.