My first instinct was to group them by 'good vs evil'—Puff and Toothless are friendly, Smaug is villainous, and Drogon is... complicated. That didn't work. Then I tried 'animated vs live-action', but Draco is Sean Connery doing voice work, which muddied that theory.
I stared at the list again. Puff. Toothless. Draco. Smaug. Drogon. What do they all DO? They fly. They breathe fire (or plasma, in Toothless's case). They have scales and wings and... wait. They're all DRAGONS. Not 'reptiles', not 'fantasy creatures', not 'fictional characters'—specifically dragons, with proper names, from famous stories.
The genius of this puzzle is that it spans 60 years of storytelling. Puff emerged in 1963, Dragonheart came out in 1996, the How to Train Your Dragon books started in 2003, Smaug has been around since 1937, and Drogon arrived with Game of Thrones in 2011. The connector isn't era or medium—it's the mythological archetype itself.