Yes, they are both mammals, called rodents. The rodent family (scientific name Rodentia) includes rats, mice, dormice, beavers, porcupines, and squirrels. Many of them, such as the lesser-toothed small rat and the common fieldmouse, are endangered. They all have strong front teeth (incisors), which they use to slice through vegetation, such as strong grasses and tree bark - and beavers even saw through tree trunks. Like other mammals, rodents are warm-blooded and give birth to live young, which they feed with mother's milk.