You can inspect the disk and memory cache via the about:cache page.

There is also a button on the about:profiles page to go to the secondary (local) profile location that is used for the disk cache.

Firefox uses two locations for the Firefox profile folder. Location used for the main profile that keeps your personal data (Root Directory on about:profiles).

• ~/Library/Application Support/Firefox/Profiles/<profile>/

Location used for the disk cache and other temporary files (Local Directory on about:profiles).

• ~/Library/Caches/Firefox/Profiles/

Went to the about:cache page, lot of stuff. Went to Preferences cleared cache, went back to about:cache page and contents were zero. Went back to the website and still showed old stuff, not the updated content. Safari sees the new content.

I'm still at a loss.

You aren't using a bookmark to access the website ?

If you use a bookmark to access a specific page then instead navigate to this page starting with the main page or with the sign in page in case there is a problem with this bookmark.

Well, well, well... it turns out that the hosting company has caching on their server. That's why when using Firefox for site edits and logging out the edits were not being seen.

So, my issue was not due to Firefox.

Thank you cor-el for your help, especially about where to find cache on my Mac.