Hey precog, been meaning to get back here and answer this but been focussed on the study for my PPL test. Not sure where you are at pilot wise, but I am pre-PPL, so take everything I say with a grain of salt. I had the same question as you about a week before you put it up here. I was lucky, because I was involved in this exact conversation with some ATC's in person just a few days before hand...
Before I go onto try and explain how I think it works, let me say this. My solution is to give an airborne report regardless. The only real difference is stating the altitude you are passing through so ATC can positively identify you on SSR. I state the altitude I am passing through even in Class G, its become a habit.
Now, my understanding of the difference between airborne and deptarure reports is this: If ATC ask you to change frequency, the on the new frequency you give an airborne report. If you depart Class D with procedural separation into Class C with Procedural separation, you will stay on the tower frequency. As soon as you are passed off to SSR class C the tower will pass you off to BNE or MEL Centre, and they will require an airborne report to positively ID you. Even when you get a transponder code on arrival, Centre will always ask you to report altitude so they can ID you.
FWIW, just too add confusion if you get passed off from MIL Class C to civilian Class C, you have to provide a report when you enter the new Class C!! Same stuff, (BNE APP, callsign, 8500ft) and Approach will always respond with QNH.
BTW: Can anyone confirm any class D that has surveillance? If so, do they require a unique transponder code or do you still use 3000?