A blues is a musical form, like a sonata or, to switch artforms, like a sonnet or haiku or sestina or limerick. It follows a certain pattern, with most (not all!) being 12-bars, and following certain specified chord changes:
I I I I
IV IV I I
V IV I V
with most/all of those usually being the dominant seventh form of the chord.
So in the key of C, you'd play:
C-C-C-C
F-F-C-C
G-F-C-G
(although, again, those would probably actually be C7 and F7 and G7 chords)
Many country songs are in the blues form, but most (I believe—I'm far from an expert here) more traditionally adhere to the 8-bar structure, with a separate chorus and sometimes a bridge or two.
So the incendiary first Elvis 45" had a blues ("That's All Right, Mama") and a country song ("Blue Moon of Kentucky"), a pattern I believe he would keep for pretty much all his Sun releases.
So to go back to your original question, not everything that BB King, say, played was a blues, even if it was always bluesy. Whereas Pat Boone, say, could play a blues but it sure as hell isn't going to be bluesy.