Genus is a taxonomic rank below family and above species. It groups together closely related species.
Reptiles are a much broader category, encompassing orders such as:
* Squamata: Lizards and snakes
* Testudines: Turtles and tortoises
* Crocodilia: Crocodiles, alligators, caimans, and gharials
* Sphenodontia: Tuataras
Each of these orders contains multiple families, and within each family, there are multiple genera. For example, the American alligator (Alligator mississippiensis) belongs to the genus *Alligator*.
So, it's incorrect to say that all reptiles belong to one genus. They belong to many different genera within their respective orders.