A tetrapod is any member of the taxonomic unit Tetrapoda (which is defined by descent from a specific four-limbed ancestor), whereas a quadruped actually uses four limbs for locomotion.
This last meaning includes certain artificial objects; almost all quadruped organisms are tetrapods (one exception is some raptorial arthropods adapted for four-footed locomotion, such as the Mantodea.
[3] In July 2005, in rural Turkey, scientists discovered five Turkish siblings who habitually walked on both their hands and feet.
Unlike chimpanzees, which ambulate on their knuckles, the Ulas family walked on their palms, allowing them to preserve the dexterity of their fingers.
Also by NASA JPL, in collaboration with University of California, Santa Barbara Robotics Lab, is RoboSimian, with emphasis on stability and deliberation.