Thanks for this question Scooter! You are not alone in being confused by this. To say that a blues song is "In the key of..." is somewhat deceptive. That information only tells you what the I chord is (and therefore what the IV and V chords are as well).
A blues song in the key of G means that the I chord is G, the IV is C, and the V is D. That's it.
Each of those chord changes assumes a new key signature. So, when you play on the I chord (G7) you will use notes of a G major scale with a flatted 7th (F natural) - so essentially you are playing a C major scale. This is known as a mixolydian mode (playing a C major scale from G to G instead of starting on C and going to the next C).
When you go to the IV chord, you will be playing in C7 (or F major scale).
When you go to the V chord, you will be playing in D7 (or G major scale).
The "Minor Blues scale" (what many people simply call the "blues scale") is only used for melodic content, NOT harmonic content. It doesn't really belong to any of the chords and therefore can be used over all of them. Therefore, the G minor blues scale can be used to play over G7, C7, or D7, with varying degrees of tension. It does not contain the major third of any of those chords, and so you cannot tell which chord change you are playing simply by listening to the scale.
this is why i always advise students to learn licks and chords first, THEN worry about using the blues scale. Because it works over all the changes, it can be tempting to overuse it, which is tiresome to listen to.. the licks and chords all contain the important chord tones of each chord change (like the major 3rd) and thus make it sound like you are playing the changes - and they provide relief from the minor blues scale sound when mixed with it.
As I am writing this I am realizing that these are simple concepts but surprisingly difficult to spell out clearly through text! I will try to address this at the next Office Hours (#21) on Sunday.
Great question though!