Anyone can explain the difference between the "no signal" and "disconnected" warning on the P3.
When do they occur and why?

Thanks in advance

I believe Disconnected means the remote and the tablet are not connected yet via the USB cable. This happens to me when I start the pilot app before turning on the remote. No signal is communication between the bird and the remote. This happens to me when I have turned on the remote but not the drone. It goes away a few seconds after I power up the P3.

I agree with Rigworker.

I tested the following:

With P3P+Controller+Tablet powered on and ready to fly, I unplugged my controller-tablet cable.  "Disconnected" is reported on screen.

With P3P+Controller+Tablet powered on and Ready to Fly, I powered off my P3P.  "No signal" is reported on screen.

So, translate that to these message appearing while in flight.  Disconnected should indicate you still have control of the bird (controller is still talking to P3), but you may have a problem with your app, or your tablet/phone.  You can still fly line of sight, in P_GPS your P3P will hover if you offer no stick input, giving you a chance to restart your app.  Or you fly it back line of sight if that is an option.  

And while "disconnected" seems somewhat clear, the problem of no signal is less clear.  You can see in this thread
http://forum.dji.com/thread-23799-1-1.html

The pilot received the "no signal" message, but points out he was fully in control, but the red "no signal" message was on his screen.  I have seen this happen when my friend with big drone balls flew 1600 feet up the side of a mountain.  When his altitude maxed at 1600, he got the "no signal", but was still in control of the tiny tiny dot way up there.  He flew it home, with the "no signal" showing the rest of his flight.

DJI - please refine your messaging to clarify what components have failed to communicate.
And address the "no signal" issue.  It is clear there is signal if we can still control the P3 and fly it home LOS.