Kabardino-Balkaria is named after its native Kabardin and Balkar people. The Kabardin are a Circassian group related to the Adyghe, while the Balkar are essentially the same as the Bulgars, who migrated to present day Bulgaria. Both groups are Sunni Muslim.
The Kabardin speak Kabardian, a north-west Caucasian language of which "Cherkess" is a dialect; the Balkar speak Balkar, a Turkic language virtually identical to "Karachay." But fortunately for the visitor, all are fluent in Russian.
While not as involved in the general conflict across the North Caucasus, Kabardino-Balkaria, especially Nalchik, has been attacked repeatedly by rebel and terrorist forces. Expect a very tight security situation, realize that this is an unstable and dangerous part of the world, and make your travel plans accordingly.