Different Types of Flight Schools
Part 61 - Part 61 training is outlined by regulation, however as long as the task areas are taught, the instructor can decide how and when to teach each, although some are required to be taught before first solo.
This type of instruction allows for a lot of flexibility.
Part 141 - Part 141 flight schools are approved by the FAA. The school teaches using a training course outline (TCO), with every lesson predetermined and approved. Instructors must teach according to the TCO and each lesson must be passed before moving on to the next, that said a sequence change can be approved to progress to a different lesson than the next in sequence (before going back to the missed one) as long as the overall structure of training is not affected. This type of training is very structured.
Part 142 - Part 142 provides an alternative means, through the use of approved training devices and simulators, for meeting the experience, training, and testing requirements of parts 61, 63, 121, 125, 127, 135, or 137 and others. This rule was implemented in August 1996 as a result of an increasing use of advanced technology that has proved capable of replicating the functionality and handling characteristics of high performance, turboprop, and turbojet aircraft.