Which blood vessels carry blood away from the heart?

Arteries carry blood away from the heart and veins bring it back, and the definition is about direction, not about oxygen. That catches people out, because the pulmonary artery carries deoxygenated blood out to the lungs and the pulmonary veins bring oxygen-rich blood back, the reverse of the usual pattern. The direction of flow shapes the structure. Arteries take the full force of each heartbeat, so they have thick walls with a lot of elastic tissue and smooth muscle; the elasticity lets them expand with each surge and recoil between beats, smoothing the pulse into steadier flow further along. Veins carry blood at low pressure, so their walls are thinner and their bore wider, and in the limbs they rely on one-way valves plus the squeeze of surrounding muscles to push blood uphill against gravity. Between the two sit capillaries, one cell thick, where the actual exchange with tissue happens.

Blood pressure is quoted as two numbers because arterial pressure peaks when the heart contracts and dips as it refills.