Cathers are credited with a put-out when a batter strikes out.
(And as a pitcher's mom, I believe that is totally bogus and the catcher should only be credited with an assist and the pitcher credited with the put-out ...) If, however, the ball is "dropped" (e.g., wild pitch or passed ball) on a strike out and the catcher manages to still throw the batter out at first, then the catcher is credited with an assist and the 1st baseman gets the put-out.
In a double play, I believe, the middle player gets credit for a put-out on the first out amd an assist om the second out ... how's that for confusing?