On Boeing airplanes, flight duties are divided in PF (Pilot Flying) and PM (Pilot Monitoring). This duties are defined at the beginning of the flight because it determine the "area of responsibility" for each pilot during all the flight or for phases of flight (for example: Captain can be PF during taxi and PM during the rest of the phases of flight).
In general, the area of responsibility for the PM, include the duty of COMMUNICATIONS, so this pilot is the one responsible for talking on the radio.
During the cockpit preparation the Captain determine which pilot will be the PF and the PM for the flight (or for the each phase of flight), so in that way every crewmember knows what are their duties, and who is going to be in charge of the radio.
I don't know the exact terms for PF and PM for other type of aircraft (I think that for AIRBUS is Pilot Flying and Pilot Not Flying) but I think this flight duty division works for all types...
Hope this helps...