Aircraft categories, with respect to the certification of aircraft, are defined as “a grouping of aircraft based upon intended use or operating limitations.” This is a topic in need of disentanglement. I will focus on airplane categories to establish a concise point-of-reference.
Before today, searching for this information could be very frustrating because, officially, it falls under the heading of “Airworthiness certificates: classification,” better known as 14 CFR § 21.175. This is the only place I could find all eleven categories mentioned.