Red Dye #40 (and all FDA certified dyes) is referred to as a "Coal Tar" dye. The phrase has little meaning today but a hundred years ago it was used to describe synthetic chemicals that started out with coal tar as a precursor. It's more likely today to find a petrochemical as the original base of most synthetic chemicals, though they're so highly refined that you won't find any residual petroleum in the product.

The proper chemical name for Red40 is:
6-hydroxy-5-[(2-methoxy-5-methyl-4-sulfophenyl)azo]-2-naphthalenesulfonic acid
which is a terribly long word for a very tiny molecule. The chemical is often referred to as an "azo" dye. If you look at the drawing of the chemical below, you'll see two Nitrogen atoms near the center of the molecule (passing your cursor over the drawing will highlight the "N" on the nitrogen atoms) The way the two Nitrogens are connected together with a double bond is called an "azo" bond; this is what makes this chemical a part of the "azo" family.

Azo dyes come in all colors, though the only azo dyes used in food are in the red-yellow range.

There are other dyes with similar chemical structures to that of Red 40. The closest certified color is FD&C Yellow #6, which is extremely similar. As you pass your mouse over the diagram below, you'll be able to compare the two chemical structures.

Yellow 6 is a smaller molecule than Red40 and reflects light at a slightly higher frequency. While Red40 is described as a orangish-red color, Yellow 6 is described as a Yellowish-orange color. It's most often used to create a pure orange color in foods - just as you'll find Red40 in cherry and strawberry flavored foods, you'll find Yellow 6 in orange flavored foods.

Another similar dye which was recently banned in Europe (it's not permitted in foods in the USA) is called Sudan 1. Sudan 1 is a red dye and has a very close structure to the certified azo dyes. Pass your mouse over the Sudan 1 molecule and you'll be able to compare the similarity to Red40.

The food dye that's generated the most controversy is Yellow Dye #5, Tatrazine. Yellow 5 has been demonstrated to provoke an allergic reaction in some people and there are FDA regulations that require all prescription medications to post a notice if they are formulated with Yellow 5. (Note: There are no similar requirements for any of the other certified dyes in prescription medication)

Yellow 5 is also an azo dye and has quite a few chemical similarities to Yellow 6 and Red 40.

If you compare Yellow 6 and Yellow 5, you'll see that they're identical to the right of the azo group but Yellow 5 substitutes a Pyrazole for a Benzene ring on the left side of the molecule. This structure moves the reflected light to an even higher frequency than Yellow 6, producing a pure lemon-yellow color.

There are many, many other azo dyes similar to the three mentioned here but they are not certified for use in foods. Most commonly they'll be found in papers, textiles, plastics and other non-biological uses where bright color and stability are desired.

Lakes

Often on a label you'll see a color listed as a lake, i.e.: "FD&C Red #40 Lake" or "Blue 1 Lake"  So what's a lake? Most of the dyes in use are water soluble, which is wonderful if you're coloring a juice or syrup. It becomes a bit of a problem if you're trying to color the outside of a medicine tablet. The manufacturer doesn't want the color to run off if the pill gets a little wet. The answer is to use a dye in a lake form.

A lake is a solid, non water soluble form of a dye. It's produced by mixing the dye with Aluminum Hydroxide. By itself Aluminum Hydroxide is a safe food ingredient and it's often sold as an antacid. When combined with Red Dye #40, the chemicals form a deep red powder that can be applied to the outsides of tablets, gumballs and other solids. You may also notice this form listed in the ingredients as "Red 40 Aluminum Lake"