Being a pilot and a heavy drone user with lots of photos on here, let me chime in.
I seriously doubt that the BCC could legally ban drones. They do not have any jurisdiction of anything in the air. That is FAA territory, and that has been upheld time and time again in the courts. Legally, they cannot impose rules that supersede rules covered by the FAA. FAA has jurisdiction in those cases.
The ordinance as written above..."No person operating, directing, or responsible for any airplane, seaplane, helicopter, glider, balloon, dirigible, parachute, ultralight, or other aerial apparatus shall take off from or land on the beaches or water bodies." does not cover drones unless they are trying to cover it under the guise of "aerial apparatus". Unless they specifically say "drones" it will be challenged if something comes of it. All that will happen is that people will launch from parking lots, streets, or driveways. Most of us don't launch from the beach, anyway, because of sand. Once the drone is in the air the BCC has no jurisdiction.
The FAA does not have strict rules in place for recreational drones. They have guidelines which are the exact same guidelines that cover remote control aircraft, but they are not laws. It starts getting tricky when you go beyond line of sight, fly within 5 miles of an airport, or fly aircraft over 55 pounds.
If you are using a drone for commercial purposes, it must be registered, the operator must have a remote pilot certificate, but again, if the drone is less than 55 pounds the rules are greatly reduced.
The FAA did start a drone registration program a while back (I'm registered), but it was far too late, and I believe it was suspended as a mandatory program. Numbers that can be found show that only a tiny fraction of drones got registered. The idea behind this was to have accountability on the operators part if there was an incident as the drone was supposed to be marked with the registration number. I believe that it is still out there, but it is voluntary.
Now...back to this. The original post said that drones were added to the definition of aircraft which is redundant seeing how the definition of aircraft covers it. The ordinance says "...any airplane, seaplane, helicopter, glider, balloon, dirigible, parachute, ultralight, or other aerial apparatus shall take off from or land on the beaches or water bodies."
It does not say aircraft. It says airplane. The definition of airplane is a fixed wing heavier than air aircraft that can sustain controlled flight. Drones are not fixed wing so they aren't covered, and they don't fit the definition of "helicopter". Again...it falls back on the ubiquitous "aerial apparatus".
Personally, I'm not worried about it. As long as my drone is 1/2" in the air there's nothing the BCC can do about it.