The term republic originated from the writers of the Renaissance as a descriptive term for states that were not monarchies. These writers, such as Machiavelli, also wrote important prescriptive works describing how such governments should estructured
I dont share your particular account of canadian history at all
As per the Constitution Acts of 1867 and 1982, Canada is a constitutional monarchy, wherein the role of the reigning sovereign is both legal and practical, but not political. The Crown is regarded as a corporation sole, with the monarch, vested as she is with all powers of state, at the centre of a construct in which the power of the whole is shared by multiple institutions of government acting under the sovereign's authority. The executive is thus formally called the Queen-in-Council, the legislature the Queen-in-Parliament, and the courts as the Queen on the Bench.