Oh good God, I called the FAA:
Flight schools come in two flavors, Part 61 and Part 141, this just has to do with the parts of the Federal Aviation Regulations that they operate under. The most common and least important distinction between them is the minimum flight time required for the private certificate — 40 hours under Part 61, and 35 hours under Part 141.
AA has Part 61, has applied for Part 141 and runs under the Part 141 requirements for their students to get a pilot's license.
Both types of flight school are considered FAA Certified.
That'll be another $150, Thanks, K, Bye
Drop it already.