What is a branch of an artery called?
The main artery is the aorta, which carries blood out of the heart. The branches off the aorta -- such as the carotid artery (which goes up the neck into the head) and the renal artery (which goes to the kidneys) -- are still called arteries.
Branches off of those arteries are called arterioles. The smallest blood vessels in the arterial system (which carries blood away from the heart) are capillaries.