It's a bit more formal than that and concerns matters of State. Ours isn't as clear cut as the Europeans, where one person (usually the Consort or the Heir) will be named as Regent. Ours is a bit more messy as you have to have at least two CoS.
In the event that The King cannot undertake his official duties as Sovereign on a temporary basis due to illness or absence abroad, two or more Counsellors of...
www.royal.uk
So if Haz was in the UK and a Privy Council meeting was called, he couldn't be prevented from attending unless his name had been specifically excluded from the LP. Same for Andrew.
Anne and Edward were supposedly added to the CoS list so that Haz and PA would never be called upon.
But KC3 has left this one wide open. While he's away William is on the same level as Haz, PA and Bea. Three non-working Royals have exactly the same official rights and status as he does.