Characters (or more accurately, animals) that belong to the clade Dinosauria, which includes 2 Orders Saurischia and Ornithischia.
Note that not all reptiles from the Mesozoic era (such as pterosaurs, mosasaurs, plesiosaurs, etc) or any prehistoric reptilian-looking animals (e.g Dimetrodon) are dinosaurs as commonly mistaken, so do not add this category to any prehistoric animal that is not a dinosaur.
Also, animals within the Dinosaurs category should not be in the Dragons category simultaneously, unless it is a verse's specific mechanics (e.g. Tyrantrum is in both categories, due to being both based on the dinosaur Tyrannosaurus rex and classified as a Dragon type).
Birds do have their own category.