I have not reviewed those guides, but those calls are from different parts of the circuit.
The PilotEdge call is the initial call when somebody is fairly far away and wants to establish contact with the tower. So they pass information with full callsign, their location, intentions and the ATIS code. Tower can then issue them instructions for joining the circuit. A possible response could be "proceed to XXX, expect right hand circuit runway 24, descend 1000"
The Denham call is the last call in the sequence. It's there to inform the tower (or other traffic in case of A/G or AFIS) that the aircraft is now established on final. Since there was previous contact already, we're now using abbreviated callsigns, and since we have already established that we're talking to the tower, there's no need to address them specifically anymore. The normal response would be "G-XX cleared to land 24".