The UK and Canada are not republics. There's no need to clarify "pure democracy"as no one thinks any modern democratic country is a pure democracy. All modern democracies are representative democracies.
Since there is, more or less, no other type of democracy around when a colloquial English speaker says "democracy" they mean representative democracy. Everything else is a pointless annoying semantic game.
Representative democracy is a perfectly acceptable term. Trying to shoehorn monarchies into the term "republic" is absurd.
It's a monarchy in name only. They're both constitutional monarchies which are really strictly parliamentary systems. The actual monarch is head of state, not head of government, and the Queen has almost nothing to do with the actual running of the Government, especially in Canada (and Australia, and so on). In reality, a parliamentary system such as the modern UK and Canada acts as a republic, despite what it's named.
At this point, the Queen is nothing more than a vestigial organ. (as an example, did the Queen come out for or against the Brexit vote? Have you ever seen a head of government remain so quiet about such an important event?)
The name is exactly the thing that distinguishes monarchies from republics. Modern monarchies are democracies, as are modern republics, though some monarchies and many republics in the world are still undemocratic.
Well, I would hope the move is towards more democracy, but it seems people everywhere are eager to vote against democratic freedoms these days.
I disagree with little of the above, but I wonder how much of it is due to 'Liz 2 in particular. I can imagine a different monarch exerting a great deal more influence. They'd be perfectly able to do so. The UK's armed forces are loyal only to the monarch and not the government, for example.
Since there is, more or less, no other type of democracy around when a colloquial English speaker says "democracy" they mean representative democracy. Everything else is a pointless annoying semantic game.
Representative democracy is a perfectly acceptable term. Trying to shoehorn monarchies into the term "republic" is absurd.