Climate control means you have control over:
The temperature via a thermostat, which is then maintained by the air conditioning system.
The option to turn off the air conditioning system, and just run the fan/ventilation.
AC only means:
There is either a split or a wall air conditioner, which you can set to simply cool the room. There are no other options available. In these rooms, you generally have a separate fan as well if you just need ventilation and not cooling.
It is rare (although not uncommon) to have rooms where the temperature is centrally controlled by the management.
In all cases heating is a separate issue. It is extremely rare to find central air conditioning systems where here is also provided (unless you are staying in a private villa or a suite/penthouse). In the vast majority of hotel rooms, heating is provided separately via either a space heater, a fan heater, or a radiator.
A ceiling fan is more common in tropical climates (in my visits to Europe I have yet to see a hotel room with a ceiling fan). I these tropical climates the temperature (and air humidity) can vary greatly between day and night. AC system's efficiency drops as the air humidity rises.
So in summary:
Air Conditioning Only = you can control how cold the room gets manually.
Climate Control Only = you can set the temperature (generally, there is a limit on how cold you can set it), and the system regulates the temperature. These systems are more automated and slow to startup and cool the room.
Climate Control and Fan = this means, that the central system has no ventilation (fan) option. This may mean that the AC system is not centralized, but provides a thermostat and automatically turns off/on as required. Either way, ventilation is a separate function.
AC Only = a traditional setup, with only cooling that is manually adjusted. The good point of these rooms is that they can be cooled very quickly, as you have your own dedicated AC unit.
AC and Climate Control = I have no idea why they have this, because I have yet to see anywhere a climate control system that didn't have air conditioning.