Black and gray is a highly traditional style and ideal for portrait tattoos and any design that represents the past in any way. Black and gray tattoos are actually done in all black, but the shading becomes so light that it appears gray, and white ink is often used to highlight certain aspects. The term "mural" simply means the tattoo is of an object or person and does not have any letters, numbers or any other script.
Script tattoos are designs of letters, numbers or any other characters that imply language. There are multiple fonts and styles for scripted tattoos, with differing levels of detail and size. A script tattoo can be a single letter or several sentences, depending on preference, though be advised--the longer the script is, the smaller the letters will probably need to be, which will inhibit the amount of detail they can have. Some script tattoos are small enough to fit on your knuckles, while others are large enough to span your back.
A color mural is the same as a black and gray one, except for one obvious difference--the image incorporates color instead of just varying shades of black. Colors can add a level of vibrancy to the design and are particularly appropriate for any design with opposing elements, such as fire and water. In fact, many images are contingent on color. For instance, without specific colors, a French and Irish flag would look identical and there would be no difference between a ruby and a sapphire.
A cross section tattoo is an image made to look as though it's underneath your skin instead of on top of it. Certain areas of your skin, throughout the design, are left blank and tattooed with frayed edges as though straining to cover the tattoo. The style is meant to portray the inner qualities we all possess or at least wish to, such as an animal's fur, a superhero's suit or even a bio-mechanical circuit board.