The rating metric is a score based on average user rating and number of ratings. Our process expands upon a formula created by /u/tornmandate who wrote a detailed article that explains the complexity of ranking items. Because the Torn scoring formula pulls scores towards the midpoint based on number of ratings, we apply a global adjustment back onto the score.
The popularity metric is for gauging flavor of the month based on user interaction.
Movie and TV popularity is sourced directly from TMDB. You can read more information about how they derive popularity in the TMDB API docs.
Video game popularity is derived from hypes and follows which are sourced directly from IGDB. You can find how they define hypes and follows in the IGDB API docs.