It is quite a weird set up in the Channel Islands because they have quite a complicated legal structure and are only “part” of the UK.
The channel Islands do not belong to the UK - they belong to the Duchy of Normandy. The Channel Islands are outside of the EU but half in and half out of the UK, hence no VAT.
Told you it was complicated!
Not sure I understand the rest of your question though about how it works in Europe/non-Europe. If you are a UK business and you supply goods to an overseas business within the EU you can zero rate the supply if the customer is a business. If it is not a business then you must charge for and account for VAT. If the place of supply is not the EU then you neither charge for nor account for VAT.
Have I understood your Q correctly?
Steve