I think at one time "western" music was a big subset of "country & western", in the heyday of Gene Autrey, Roy Rogers, Tex Ritter, Wilf Carter, etc. These people sang a lot of "cowboy" songs, as well as what we'd think of as mainstream country. Nowadays most of the "hat acts" don't sing western songs -- the costuming is the only relic of "western" music remaining in "country" music. I can think of a few exceptions: Michael Martin Murphy, Ian Tyson, Riders in the Sky, Don Edwards, Red Steagal, David Wilkie... But for the most part I'd say the term "country & western" nowadays is outmoded -- there are lots of "country" singers, a few "western" singers, and little crossover.