We have a Free version of our plugin that is licensed under GPL and published in the WordPress Plugin Directory.
We also have a Pro version of our plugin that we offer to our Free users, that adds extra functionality and features. To get the Pro version, the user has to create an account on our website, pay and download a .zip file of the Pro version of the plugin.
According to GNU, as the copyright holder I can release the same software under two different licenses.
I don't consider our plugin to be a derivative of WordPress, because it was built from scratch: We didn't fork anything from WordPress and built a new version of it - it's brand new work.
Does the Pro version of my plugin that the user downloaded from my website must be licensed under GPL as well? Can I license it under a proprietary license?