There are no rules as to what title you have and what jobs you are expected to do as this will depend on the size of the operation. If you are overloaded then it is up to you to tell your manager that help is needed for example you usually get the rostering department making the hotel bookings. Your job would involve finding the fuel figure required for the flight with the production of a flight plan, but not usually arranging the refuelling itself.
A Dispatcher would usually be providing the flight plan, weather and NOTAMs to the crew and monitoring the flights if you have the means. If there is no separate navigation department in your company it may also mean preparing routes and applying for overflight clearances if necessary.
p.s. The plural of aircraft is also aircraft.