What's the difference between the normal version and the Clean version? The project doesn't say.

The Clean version is updated more frequently, has some extra features, and does not use Google Analytics:

https://gitlab.com/magnolia1234/bypass-paywalls-firefox-clea...

Bypass Paywalls Clean releases: https://gitlab.com/magnolia1234/bypass-paywalls-firefox-clea...

Bypass Paywalls releases: https://github.com/iamadamdev/bypass-paywalls-chrome/release...

Currently, the Clean version has 13,750 users while the original version has 9,864 users on addons.mozilla.org, so the fork might turn out to be more popular.