Gray hair is hair that grows in without natural pigment or melanin in it. Because it is missing pigment, the gray hair is lighter in weight and less manageable. It can be permed (curly permed/soft curled) or relaxed, texlaxed/texturized. Pictured is coarse, gray hair that started off as natural Type 4c hair from a woman with black hair and some gray hair. (Less than 25% gray) It is now texturized or texlaxed. So it went from extremely tightly coiled "z" curls to a "z" ripple!
Type 4c curl patterns do not have to be coarse. Type 4c curl patterns can be fine or medium in texture/strand diameter.
Gray hair does not have to be coarse to still be difficult to manage and hard to color. In order to keep gray hair shiny and "non-yellow," voilet base shampoos or conditioners have to be used as needed. Typically, chemicals and heat can cause gray/white hair to yellow. According to the color wheel, if you add some blue and red (i.e. violet), then it neutralizes the yellow color.