I'm a simple man, so here's an (over?) simplified answer...
Consider a 12-bar blues in A Major, ie A, D and E chords. These chords all come from the key of A Major, so you could use the A Major pentatonic to solo over them. However, "Blues" is a mix of major and minor tonalities, so you can get away with using the A Minor pentatonic, because over the years our ears have become accustomed to it, and blues licks blur the differences between the two.
Now consider a 12-bar in A Minor, ie Am, Dm and Em chords. These chords all come from the key of A Minor, so the Am Pentatonic will fit perfectly. Now, you might argue that Am is the same as C Major, but... the "A-minor-ness" of the chords keeps pulling our ears back to Am.
Now we'll play a Country song in C major, with the chords C, F and G. These chords are from the key of C Major, so the C Major pentatonic will work fine. But, isn't C Major penta the same notes as Am penta? Why, yes it is, but... the "C-major-ness" of the chords pulls our ears back to C major.
So, we're using the same scale (C maj / Am penta) with a different backing. When we solo using these scales, we must emphasise different notes in the scale, to get it to fit over the chords. This is why you can't play your minor blues licks over a country song - the licks emphasise the "wrong" notes.
I liken it to interior decorating - the chords are the background, like the colour you paint your walls. The notes of the scale are the items you place in the room - cushions, curtains, ornaments, pictures, in colours to complement the walls. If you change the colour of your walls, you have to change the colours of the items in the room.
So, don't play the blues in a pink room - it just doesn't work!
(Other scales are available, but that's verging on jazz...

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