There are only a few breeds that are in one color. They may have the color as part of the name (like Russian Blue) but in most cases any color (calico, blue, etc) is simply a color and many breeds have that color.
For awhile British Shorthairs used to be called "British Blues" as mostly blues were shown, but they've always come in many colors, so the "Blue" was dropped and the cats are called British Shorthairs.
Other cats like Havana Browns only come in brown. Korats are another "one" color breed - blue. For Russian Blues (I did breed them at one time, so know about the history) they are unique cats. Not the typical solid blue/grey color. They have short thick fur (you should be able to press a thumb down and the fur to hold the indent) with SILVER tipping/highlights. They also have green eyes (most blue cats have gold eye color). Korats are similar with a short tight coat and silver color on the ends.
BTW there are "White Russians" that occasionally show up - these are blue point russians. They occur because at one time Russian blues were bred to siamese and so the pointed gene is in the lines. I've only seen a white russian one time (other then in pictures). Its not encouraged and any that show up are spayed/neutered and placed as pets.
Russians are quiet cats, shy, and more of a one-person cat. They don't like a lot of noise, etc. and that's why you don't see them in shows very often. Once in awhile you have an outgoing Russian (my neuter was) but for the most part they prefer to stay at home and not show off