Bits of paperwork will need to be amended: It is now "His Majesty's Government" and so forth
There are transitional matters to arrange. The funeral and coronation are state affairs and are organised by the government - and of course members of the government will not be doing other business when they are attended these events.
The Queen has a weekly audience with the Prime Minister. It is clear that she has not always been well enough to receive the Prime Minister. Surely the King will want to hold these meetings.
Other matters which had been done by her household or by members of her family will now be done in person by the King. The King will open parliament but he already did this. Next time, he gets to wear the
silly hat crown.
Similarly, the government uses the royals to project soft power: "Be nice to Britain, and we'll let your head of government have dinner with the King". (Trump, for example was flattered by having a State reception with the Queen). The Queen has been too unwell in recent months to attend such events - which were anyway impossible during the pandemic. The new King can resume a more active diplomatic role.
Finally, Charles has different priorities and interests from Elizabeth. He is personally much more concerned about the environment, for example.
This is not like the Who lyric, because there is no claim of being radically different. The Who are criticising politicians who claim to represent radical change, but do nothing. The monarchy represents continuity not change.