Not quite correct. The island of Great Britain is the big island which comprises most of Scotland, England and Wales.
United Kingdom comprises (for now) Scotland, England, Wales and Northern Ireland.
So the Isle of Man and the Channel Isles (Jersey, Guernsey, etc) are part of Great Britain, but they are not part of the United Kingdom.
There are many smaller islands which form part of the British Isles and the United Kingdom but not of Great Britain, for example Skye (Scotland), Anglesey (Wales), Wight (England).
Isle of Man and the Channel Isles are part of the British Isles but not of Great Britain.
They are not part of the United Kingdom but as they rely on the United Kingdom Government for foreign affairs they are "British Crown Dependencies".
All very complicated and confusing!
Regional Director for Scotland for Clan Cunningham International, and a Scottish Armiger.