Arteries and Veins. As we stated on the previous page, What Is High Blood Pressure , arteries and veins are both part of the circulatory system and carry blood from the heart to the lungs and to all other parts of our bodies. Both are very important in maintaining our blood pressure.Though they both carry blood through our bodies they are very different and are even made of different tissue and perform their own functions in specific ways. Arteries. Arteries carry blood which is full of oxygen away from the heart.Arteries have three layers of tissue-the outside and inside layers are made of a connective tissue which covers the muscular middle layer of smooth muscle, and elastic fibers. These tissues provide a smooth path for our blood to flow through.oth are very important in maintaining our blood pressure. Though they both carry blood through our bodies they are very different and are even made of different tissue and perform their own functions in specific ways. Arteries. Arteries carry blood which is full of oxygen away from the heart.