New Mexico is famous for its chiles and its chili, both come in forms green and red. Some divide the state into the southern green-leaning part and the northern red-tending area, but it ain't that simple. Most restaurants offer both - green or red chile poured over your enchiladas or your chile rellenos or really anything you can think of.
So what's the difference? Time. Time is the difference between green and red chiles in New Mexico. New Mexico chiles - such as the famed Hatch chiles grown in and around Hatch, New Mexico - are often just called New Mexico chiles and come in many varieties.
How to find them? It's best to order them from a New Mexico source, but when they're in season many specialty markets will carry real live "Hatch green chiles." While these prized chiles are closely related to Anaheim chiles, they are often labeled "poblano chiles" otusdie fo New Mexico (and, of course, actual poblano chiles are often labeled Anaheims). You need to go by how they look rather than how any market might label them.
In any case, they start green - when many people harvest and roast them - and turn red as a they ripen. Some people roast them red, but more commonly they are hung to dry before being ground into a chile powder as fine and flavorful as you can imagine.
Different strands - Sangria and Big Jim are two common ones - offer varying levels of heat for afficionados.