Please reread what I wrote. I hope it's pretty clear.
Actually, the term "carry-on" has a specific meaning when it comes to what you can bring into an aircraft cabin. Airlines usually allow only one carry-on. Spirit Airlines charges for a carry-on.
In addition to a carry-on, you can normally bring on a personal item (such as a purse or computer bag that fits under the seat), assistive devices, and various miscellaneous things such as a coat, a camera, and food for consumption on the plane. These other items are not considered carry-ons.
Saying that a CPAP is a carry-on suggests that a passenger with a CPAP cannot also bring a bag for the overhead compartment (because only one carry-on is allowed). But that's not the case.