Music theory is probably a bigger part of the craft of Jazz than it is of classical musicians. The symphonic player interprets the work of a composer, note for note. The jazz person does that too, but during a solo the jazz player also becomes a composer. This can't happen in any honest way without an intimate understanding of how sound and time are organized.

It's important to simplify. There are tons of tunes, tons of chords, twelve keys, fast and slow, lots of ways things can happen. As a jazz improviser, the need is to comprehend, to recognize, to organize, then to simplify, to reduce things to their simplest components. There's no time for conscious thought to get in the way of flow. When Joe Pass was asked what he thinks about when he plays, he answered, "Nuthin'."

When playing jazz, the chords of a tune are clues that indicate which tonalities are relevant. It seems like the possibilities are infinite, but they aren't. Over time a player can decode the clues. Tonality seems to give chords a sort of gravity, magnetism, attraction, whatever, organizing them in certain ways, into patterns that are recognizable, especially if the player knows tunes.

A scale is a series of tones that establish tonality. Tonality is all the sounds one scale can make, either as melodies or chords. Some sounds can only be made by one particular scale. Other sounds can be made by several scales. This is all the stuff you have to get straight.

I boil everything down to parent scales. The idea of modes to me means that a scale has seven different sounds, root to root, second degree to second degree, third to third, and so on. Thinking backward, if those seven modal sounds all have the same notes, I'd rather give seven sounds just one name. Why think F aeolian, Bb dorian, Eb mixolydian, Ab Ionian when all of it is Ab major? Simplify.

Chords have parent scales, too. Fmi7 is spelled F, Ab, C, Eb. An Eb major scale has all four of those notes. So does Db major and Ab major. So does C harmonic minor and Eb melodic minor. Good jazz musicians know this kind of thing. So which parent scale is the right one? That's what chord progression is for.

Progression are sequences of two or more chords, all of which come from the same scale. Bb7/Eb7 is not a diatonic progression, because the is no one diatonic scale that generates both chords. But Bb-7/Eb7 is, because both chords are generated by Ab major. The gravity, magnetism, and attraction of sound makes chords tend to move by fourth, or stepwise, or sometimes chromatically. Fourth motion is the strongest one. That's what goes into recognizing progression.

Now the other thing that's going on all the time is that I work on my lines, creating phrases that I like to hear. I do that in all the tonalities in ways that reflect the various chords and chord progressions encountered in tunes. It's not enough to know that F-7/Bb-7/Eb7/Abma7 is generated by the Ab major scale. The improvisations you execute have to sound good to the discerning ear. Ideally, the listener actually sort of hears the chords, even if they aren't being played. On top of that, the jazz ear expects to hear the extensions, substitutions, rhythmic phrasing and ornaments that make the line swing.

So here are the first eight bars of "All The Things You Are" the way I hear it, chords followed by tonality:
F-7 Bb-7 Eb7 Abma7 is all Ab major. If I want to hear altered extensions on Eb7 the tonality is E melodic minor. If I want a tritone sub on Eb7 I hear it as an A7 chord and play a D major tonality on it. Then Dbma7 in the fifth bar is Db major. D-7(b5) is Eb major (some interpret it as F melodic minor) G7alt is Ab melodic minor. Cma7 is C major.

That's a lot of thinking to eliminate from the process. Making special studies of hearing altered dominants, tritone substitutions and minor II-Vs clears up a lot of that. And remember, on every tonality, work on those lines. I write a lot of etudes in my notebooks to deal with that.

The truly great players may be in fact thinking of "nuthin'," but I generally am happy enough if all I need to think about are parent scales. When I really know a tune cold I don't even need to do that. Then I'm real happy.