Dear @stephunique,
Thank you for the topic.
Please find the answers to your questions below.
1. The difference between the quizzes on 2 pages can be connected to the cache (if it is available on the site).
Most presumably, you have enabled the Show average rate option from the Quiz Settings, and as there is a cache on the website, the updated version was displayed on the new page.
However, as there was a cache generated on your site before, the quiz was not updated and the page HTML was displayed without any updates.
See the screenshot below:
To be sure of this, please provide us with the links to both of these quizzes. Also, please clear all the caches and check the case.
2. The most popular can be considered the quiz that has been passed the most by the users.
That means the one with the most results.
3. As to the following part.
<<how do we actually rate it?
How can people vote for the quiz?
If you want the quiz takers to rate the quiz, then, please head to the Quizzes > particular quiz > Results Settings Tab and tick the Enable quiz assessment option.
After this, the users can rate the quiz and leave feedback after passing the quiz.
See the screenshots below:
Thank you.