Safari - does "Clear History" also remove stored data?

I wanted to remove all website data.

Instead I clicked "Clear History." Which I think mainly removes the list of sites I've been to.

Then I read to actually remove those sites' data, you have to click "Remove All Website Data." And then delete the websites that show up in that list as having website data on your machine.

However, since I had already clicked "Clear History", all those websites were gone from the "Remove All Website Data" list. So I couldn't select them to clear their data.

Does that mean that "Clear History" also removes all the website data too? Or is that data now stuck on my machine somewhere and I can't delete it?

Apple's own article seems to say "Clear History" does not remove website data, like cookies and cache, etc.

I want to delete all cookies, cache and any other stuff left behind by those websites. And start fresh.

https://support.apple.com/guide/safari/clear-your-browsing-history-sfri47acf5d6/mac