A quadruped is an animal having exactly four walking legs.
While the argument may be made that "every limb, including an arm or wing, is just a modified leg", such a sense of "quadruped" is better described as a tetrapod, evoking the taxonomic unit tetrapoda the vertabrates with quadruped ancestors, including mammals, some reptiles, amphibians, and birds. The distinction is particularly important in the context of bipeds having two legs, adapted in gross anatomy and neurology a bipedal gait, and of quadrupeds having, in their arm- and wing-homologous forelimbs, markedly different characteristics that a leg must have, whether adapted to a role in a bipedal or quadrupedal gait.