Some callsigns are in the format (Something) "(Number)-(Number)". Other callsigns are in the format of one word, such as the famous examples of Pete "Maverick" Mitchell and Bradley "Rooster" Bradshaw. At what times are these callsigns used?
Section 2-4-20 of the 7110.65 describes how callsigns are to be used.
Tactical pilots of the US Navy and Airforce commonly give each other "callsigns", but they are actually just nicknames. They are used only for inter-flight communication with other pilots on discrete squadron frequencies. They are not used with ATC.