It doesn't just ''happen to be the same people'' that are members of both. It's always the same people that are members of both.
I as a person can very well have two different jobs that are totally not related. But the fact remains that if I were to quit one of these jobs, someone else could fill my spot. That doesn't apply to British and Canadian monarchy. If the British Monarch chooses to resign, we loose our Canadian Monarch. You can defend the independence of the titles as much as you want, that doesn't change the fact that they are inextricably linked together.
Actually, you are mistaken here.
Were Her Majesty the Queen to abdicate (and here's to hoping that she never does), Her Majesty would be required to sign instruments of abdication addressed to each of the sixteen realms, with particular reference to Her Majesty's constitutional role in each. This was the case when
Edward VIII abdicated; an instrument of abdication was sent to Canada in his capacity as the Canadian monarch. The Government of Canada was required to consent to the abdication (as Parliament was then recessed). If the British monarch resigns, that has no implications (constitutionally) for Canada; there is only an abdication when the Canadian monarch resigns.
I understand Queen Elizabeth yesterday signed the bill legalizing homosexual 'marriage' in Britain. More than anything else i think she might have sealed the death knell of the monarchy. Monarchies exist in the modern era.. and really since their inception.. as models and representatives of nobility and order.. of the highest aspirations and symbols of the nation. In recent years the monarchy has attempted to make itself an icon of family life. But, in a society where depravity and disorder are celebrated and indistinguishable from that which is honourable.. whatever relevance the monarchy had, has evaporated.
Her Majesty enacted the
equal marriage bill (note the conspicuous absence of quotation marks) with the advice and consent of the House of Lords, and the House of Commons, both of which had vigorous debates on the issue. Even the House of Lords, which has tended to be the more conservative of the Houses on social issues such as this, championed the cause. Equal marriage has nothing to do with monarchy, other than to recognise that the monarchy reigns but does not rule; the people have spoken, and the monarchy governed itself accordingly.