No - it means that Charles III is an independent monarch for two separate nations.

The monarchy is 99% ceremonial in Canada but it's important to note that the Canadian Crown isn't the UK Crown... Canada is not a dependent of the UK in anyway, simply the person that wears the Crowns is the same person.

https://en.wikipedia.org/wiki/Monarchy_of_Canada

>the Crown has had both a shared and a separate character: the sovereign's role as monarch of Canada has been distinct from their position as monarch of any other realm,[n 4][16][65][66][67] including the United Kingdom.[n 6][69][70][71][72] Only Canadian federal ministers of the Crown may advise the sovereign on any and all matters of the Canadian state,[n 7][70][73][74][75][76][77] of which the sovereign, when not in Canada, is kept abreast by weekly communications with the federal viceroy.[78] The monarchy thus ceased to be an exclusively British institution and, in Canada, became a Canadian,[40][79][80][81] or "domesticated",[82] establishment, though it is still often denoted as "British" in both legal and common language,[40] for reasons historical, political, and of convenience.

It's not just theoretical -- IIUC, if Charles, William and George get hit by the same bus, Charlotte would become Queen of the UK while Louis would become King of Canada.

I'm sure that in that scenario Canada would quickly update their primogeniture laws to give Charlotte primacy over her younger brother, but at the moment the primogeniture laws of the two countries are different.

I guess if going in the UK gets tough the royals could move somewhere else to reign. Sigismund was king of Sweden and Poland, though he couldn't maintain both. Maybe we'd need some drama with usurpers and uncles and so on to keep the populace entertained. Without the civil war part...