Absolutely, that’s part of the secret - by using it in its entirety you get a lot more to play with (pun intended)!
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This is a GREAT but also HUGE question!
But in short - yes there are two parallel (not really opposing) approaches to improvisation - though they do kind of come together at points as well.
I suggest students learn Blue or Major improv independently - they kind of come together with modal playing - but that gets into more jazz or modern Blues. Traditional Blues really is language based (licks).
It is, of course, more complex than this and arguments and alternative views, but this is how it seems to me!
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Thanks everyone for the answers