According to the FAA, a child who weighs at least 40 lbs. (regardless of height) can safely sit in an aircraft seat restrained by the seat's lap belt. That is, they will be just as safe as the adults sitting next to them.
The recommendations for aircraft use and automobile use are different, because the vehicles are very different, as are the stresses and impacts that one can experience. The FAA makes the rules for seats used on aircraft.
Under the FAA definition, a carseat is only defined as a disallowed "booster" if it lacks any upper body restraint system.
If you have a convertible seat that still is being used with the full harness attached, then the seat is not considered a "booster" under the FAA definition. As long as the harness is still in place, and the "approved for use in aircraft" sticker is in place, the seat can be used in an aircraft if its occupant weighs less than 40 lbs.