Just 2 separate methods of tracking your qualification for elite status.
Every mile flown on AA (and AE, AX and Alaska) earns one elite qualifying mile, regardless of fare paid. But q-points are awarded depending on the fare class (and hence, fare paid).
Some fares (F and J, for instance) earn 1.5 q-points per mile flown, allowing for faster elite qualification if you fly on more expensive fares. Really cheap fares earn only 0.5 q-points per mile.
The two schemes are not intermingled or combined - you become EXP if your year to date points total 100k or your year to date miles total 100k.
Q-points were added as a way to reward higher-yield pax while still awarding elite status to loyal butt-in-seat pax (on any fare).