No, they're not the same kind of tissue, but they can be interchanged, to a degree. For coronary artery bypass, the saphenous vein (a leg vein) is often used.

Arteries have thicker walls than veins, and a thicker layer of muscle inside them. Except for the pulmonary artery, arteries lack valves. Veins are thinner-walled, with a thinner muscle layer. They also have valves. These valves prevent blood from pooling and flowing backward (gravity and all that), and, because venous pressure is lower than arterial pressure, the valves "help" pump deoxygenated blood back to the heart.

Edited to add that veins and arteries can also purposefully be connected together to create an arteriovenous fistula, for dialysis access. Arteiovenous fistulas can also occur naturally, as congenital defects.