What’s service does ATC service include? As I’ve studied on ATC service and airspace class by referring to ICAO Annex, I have some doubts on ATC service. 

According to ICAO Annex 11, Class D airspace is defined as “IFR and VFR flights are permitted and all flights are provided with air traffic control service, IFR flights are separated from other IFR flights and receive traffic information in respect of VFR flights, VFR flights receive traffic information in respect of all other flights.”

When referring to other definition such as ATS service, It is divided into ATC service, flight information service and alerting service. And I think separation and traffic information service are included to ATC service of ATS service.

So, when I read the definition of Class D airspace that IFR and VFR aircraft are provided with ATC service, I think separation and traffic information service are also provided because these are the ATC service. However, as you guys know, although ATC service is provided to all VFR and IFR in controlled airspace, separation and traffic information are selectively applied depending on airspace class.

To sum up, I want to know what ATC service includes and whether traffic information and separation are one of ATC service or not.
Air traffic control service is a service provided for the purpose of:
  
  
  preventing collisions:
  
  
  between aircraft, and
  on the manoeuvring area between aircraft and obstructions; and
  
  expediting and maintaining an orderly flow of air traffic. 
  
  
  (ICAO Annex 11)


When saying a flight is provided with ATC service, it is just another way of saying that it is a controlled flight. That is, a flight where the pilot can't just do what they want, because the flight is subject to an ATC clearance; the ATCO will clear the flight to follow a certain route and fly at a certain level.

Importantly, all controlled flights are coordinated as long as they remain in controlled airspace. This ensures alerting service throughout the controlled portion of the flight. This coordination also extends to military units (so we don't have a repeat of Korean Air 007). Controlled flights are also provided with flight information service (traffic info, weather info, info on nav-aids etc.)

As stated in the quote above, ATC service is provided for the purpose of preventing collisions. However, actual separation is not necessarily guaranteed to be provided by the ATCO. The class D airspace you mention is a great example. Separation is only guaranteed to be provided by ATC for IFR-IFR conflicts. In other cases, it is ultimately the responsibility of the pilot* to prevent collisions, which they are able to do based on the flight information service provided.

*: the controller can still decide to provide separation, but is not required to do so.

Note that separation on the manoeuvring area (which includes the runway) is provided regardless of airspace class.