> Google is a third party when it is about you (first party) using a Mozilla service (second party).
Sure, but that is not the distinction I was making though. Google Analytics is a first-party tracker in the sense that it sets a cookie on the same domain that the script is loaded on. Contrast this to a third-party tracker which sets a cookie on its own domain, and as such the same cookie will be reused for all websites using this third-party tracker.
> it tells Google what they looked at and when
As far as I know only Mozilla has access to the data collected through their Google Analytics account. Third-party trackers, however, often aggregate collected data across a wide range of websites, and might sell augmented, highly profiled user data to advertisers. I have not seen any reports of Google using Google Analytics in such a way, but the data is nonetheless stored on their servers, so you will have to trust that they won't abuse their power.
EDIT: As mentioned by throwaway9d0291, it seems like there are settings for enabling or disabling the sharing of Google Analytics data with Google. Not sure if this is opt-in or opt-out though, but this means that it possible to use the service without Google using the collected data.