Include the analytics count in our community home page

That’s the branch of Discourse you have installed.

tests_passed is the default one that you would be on if you’ve followed a standard install. It picks up all the fixes and new features as soon as they’re available (new things are added every day), and you can update your site any time from the /upgrade page to get them for your site as often as you think you need to.

stable is a more static version that gets a major release twice a year (roughly at the end of January and July). This one wouldn’t get all of the new features and updates of the current cycle until the cycle had completed.

You can read more about the different types here - Why does Discourse always install "beta" versions by default?