Hi Windshear
You use the aircraft's full callsign eg, G-ABCD until ATC abbreviate it to G-CD. When you change to a new frequency, that ATC unit may already be working another "G-CD". If this were the case the other aircraft would also be asked to use its full callsign to avoid confusion.
So on first contact, including going from Tower to Approach; or vice-verse, full callsign.
In the UK, and most other European countries, the country prefix is used and the last two registration letters in the abbreviated callsign.
Abbreviations to the last three letters of an aircraft's callasign do occur in countries such as Canada and New Zealand. No doubt there are others.
Hope this helps
D 'n' H