Bats are not rodents. All bats belong to the scientific group Chiroptera, the second-largest grouping of mammals after the group Rodentia itself. The most obvious difference between bats and rodents is that bats can fly and rodents cannot.
Bats have many adaptations that make them very different from rodents or any other group of mammals. Their paws evolved into membranous wings, and they have relatively massive chest muscles to power these wings through the air. Bat ears and brains process ultrasonic chirps into a three-dimensional picture of the environment. This ability to see through sound is called echolocation. Rodents lack all of these key features.