Quadruped is used for living animals, not objects with four support points. Most quadrupeds can run faster than two-legged creatures.
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Not Bipedal
Quadrupeds and bipeds are opposites; 'quadruped' highlights the animal doesn't walk on two legs. Birds are generally not quadrupeds.
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Walking, Not Crawling
Quadruped animals walk with their legs, distinguishing them from creatures that crawl or slither. Turtles, even with four limbs, aren't always considered quadrupeds.