The two axes are
- Social--essentially a binary axis of "plays alone" and "plays with others"
- Literal--"free style or creative" on one end and "plays it like it's written" on the other
There is nothing judgmental about this system, nor is one's position in a quadrant fixed. I, for one, can be found in quadrants I, II, or IV depending on when you snap the picture.
I do think, however, that your dominant quadrant can shape how you play. For example, I spent most of my life in quadrant I, playing folk songs on the guitar by ear and writing my own music. When I started learning Dobro, I stayed in that mode pretty much exclusively. As such, I have a tendency to want to maintain a full picking pattern as "background" and pick the melody line out as I lay down a carpet of notes around it.
I have a buddy who is primarily quadrant II. He's quite literate on piano, and although he learns guitar songs by ear, he can play a very literal rendering of the source he learned the song from. I don't do so well at learning by ear because I have a dyslexic ear. 1. 3. 5 and 1, 5, 3 sound alike to me. Or if I get 5 out of 7 notes, well that's as good as all 7. Unfortunately, playing by ear has been my learning style most of my life.
I've started operating in quadrant IV a lot--participating regularly in bluegrass jams, and this has driven me to quadrant II. I try to learn a song from a jam, but I can tell I'm not quite "getting it." So I have started to read music so that I can get the melody line correct. Then I arrange it for the Dobro. But my quadrant IV perspective has made it so I am not as compelled to lay down the carpet of notes any more. I'm getting used to having others establish the full body of a song, and I am learning to add grace licks or transitions. And since the Dobro does not play certain chords very well (open tuned to a G-major), I'm learning to pick through those awkward chords with delicate melody or harmony lines rather than playing robust multi-string chords.
I'll probably never get to quadrant III, although I envy those folks. That's where most session musicians operate, you know, folks who get paid to play. It's OK, just moving into II and IV has rejuvenated my appreciation of music and my enjoyment.
Be careful about quadrant IV, though, that's a real addictive neighborhood.