If we use a CMS that is covered by the GPL (v2), do we have to re-release the source code of the CMS if we make modifications to the core?

The GPL v2 states:

The GPL does not require you to release your modified version. You are free to make modifications and use them privately, without ever releasing them. This applies to organizations (including companies), too; an organization can make a modified version and use it internally without ever releasing it outside the organization.

But if you release the modified version to the public in some way, the GPL requires you to make the modified source code available to the program's users, under the GPL.

The grey area for me here is the part that states "if you release the modified version to the public in some way" - does displaying a website to the public count as "releasing it to the public"?

What about if a custom plugin is written which integrates with the CMS - are we required to release the source? Does this count as a modification?