Definitions we need to clear up.
I see comments and statements and articles and tweets about the status of the commonwealth and the realm and territories and the United Kingdom and it's pretty clear that the majority of people don't know the differences between them. I know that this might seem petty or redundant for some people but hopefully it can help educate some others since the media doesn't help when they use these terms interchangeably despite the fact they are different entities completely. So, in an effort to clear this all up, here are definitions of all of them (and yes, please use this as a reference if needed, especially people in the press).
The Commonwealth vs Commonwealth Realms
The Commonwealth - (also called the Commonwealth of Nations) A voluntary political association of 56 members states united by a common to promote democracy, human rights, good governance, the rule of law, civil liberties, equality before the law, free trade, multilateralism and world peace.
Commonwealth Realms - (also called Realms and Territories) Sovereign states in the Commonwealth of Nations who have a monarch (King Charles III) as head of State. There are currently 15 Commonwealth Realms.
To elaborate a little more, not all members of the commonwealth are commonwealth realms (i.e. not all 56 member countries have King Charles as head of state) but all Commonwealth Realms are part of the Commonwealth of Nations.
Furthermore both King Charles III and Prince William have stated it is up to each of the realms to decide if they want to remain a commonwealth realm or if they want to be fully independent. They have both stated multiple times they will support whatever each country decides. Finally, leaving the Commonwealth Realms does not mean a country leaves the Commonwealth of Nations (see Barbados, India, etc.)
Head of State vs Head of Government vs Head of the Commonwealth
Head of State - As head of State of 15 commonwealth realms, the Monarch remains strictly neutral with respect to political matters. It is a ceremonial role and they do not hold any official power. The Monarch does not vote or stand for election, however they do have important ceremonial and formal roles in relation to the government of the UK.
Head of Government - The Prime Minister or President of each of the 15 commonwealth realms act as head of government and hold the power in running governmental business day to day.
Head of the Commonwealth - Is a ceremonial leader who symbolises "the free association of independent member nations" of the Commonwealth of Nations, an intergovernmental organisation that currently comprises 56 sovereign states. There is no set term of office or term limit and the role itself involves no part in the day-to-day governance of any of the member states within the Commonwealth
The United Kingdom vs Great Britain vs the British Isles
United Kingdom - The U.K. is made up of four countries: England, Northern Ireland, Scotland and Wales.
Great Britain - Britain is made up of England, Scotland and Wales
British Isles - The British Isles are made up of the countries of the U.K, Ireland, the Isle of Man, the Inner and Outer Hebrides, the Northern Isles and over six thousand smaller islands