Another Country Heard From

Today is International Country Music Day.  When I heard that I had some questions.  First, does the "international" part mean it's music from every country?  Turns out no, it's an international celebration of what is known as country music in the United States.

Which leads to my second question: does everyone else call it "country music" or just us?  If others do call it that (whether in English or another language) aren't they kind of offended?  How come the "country" is America?  It's like calling a baseball championship the World Series.

Also, just how popular is "country music" across the world?  It's certainly been big here in the U.S. for decades, but did it catch on elsewhere the same way rock 'n' roll and rap did?

I believe the phrase "country music" was coined in the mid-1900s as sort of an improvement over "hillbilly music." Another common phrase in the music industry has been Country and Western, or C&W, which also added all those western cowboy songs.  Though just how related were they that they get thrown into the same category?