Cabbage is a leafy vegetable staple with a 4,000 year history. It is enjoyed all over the world with over four hundred different varieties available. Some of the most common types of cabbage include the green cabbage, red cabbage and the Savoy cabbage. Napa cabbage and bok choy are two popular types of Chinese cabbage.Green cabbage is one of the most easily recognizable types of cabbage. It has dark outer leaves with paler green inner leaves.Like all varieties of cabbage, green cabbage is high in vitamin C and it also has high levels of folate.ed cabbages are another of the more common types of cabbage. Prior to cooking its leaves typically range from a deep red to a purplish color. Once it is cooked the color changes into a blue shade unless it is prepared in some form of acid, such as vinegar.