One is a movie and the other a mini series. But both are about chess or at least centres around the game.
The depiction of Chess from The Coldest Game was silly to say the least. For one thing, in The Coldest Game, the person who overseeing the game is called "arbiter", not a "judge". Also, when a player wants a draw, there is no need to pass the offer via the arbiter, they just ask the other player. Of course there are many tiny inaccuracies in the movie that would make a tournament player cringe.
The other aspects of the show is acceptable and I only watched because I like Bill Pullman's acting.
The new mini series "The Queen's Gambit" starring Anya Taylor-Joy is way better in terms of chess accuracy. All the chess openings are right, like the Sicilian Najdorf, Levenfish variation, how a simul event is conducted are all correct. I just appreciate it when film makers take the trouble for small details like that and not "inventive" when it comes to chess facts. Overall, I think The Queen's Gambit will be a worthwhile watch especially when IMDB rates this at 8.7 out of 10.