What's the difference between a Bullsnake and a Gopher Snake?

We hear this a lot. A snake is seen and some people say it's a Gopher Snake and some say it's a Bullsnake. So, are they the same thing? If not, What's the difference? I intend to answer those questions here.

We'll start with some taxonomy. Snakes (as well as all other animals) are classified by a Latin name. It looks as follows:
Genus species subspecies
If there is no subspecies recognized, it is just left off. The classification for the Pituophis is as follows:

The only species we have in New Mexico is Pituophis catenefir Gopher Snake. We have three subspecies in the state and they all intergrade. The easiest way to tell them apart is by range. Here is a range map from Calfornia Herps:

Here it is cropped to only New Mexico. As you can see a majority of the state is covered by the Sonoran Gopher Snake. The grey area is what is called an intergrade zone. This is where the snakes show similarities with two or more subspecies. Great Basin Gophers tend to have a "cleaner" pattern, some individuals have spots closer to the head. The bullsnake's rostral scale is usually taller than it is wide.