I am confused about the difference of online case form and external case form. Which one is really associated with the customer center? Which can be associated with a website that is not linked to NS?

We do not use SuiteCommerce (Magneto hosted) and do utilize online case forms with support cases flowing directly into NS and linking to a customer account by e-mail address.

Thank you, @Kathryn Klein. It seems like online case form is to external website then.