Technically Canada is a Constitutional Monarchy and a Parliamentary Democracy.
The Queen of England is also the Queen of Canada (our head of state also known as "The Crown") Canada's legitimacy as a state is based on treaties and laws signed by the Crown. The Governor General (GG) is the Queen's representative in Canada. Below the GG is the Prime Minister (PM). The Queen and the GG's powers are mostly symbolic. However bills become laws after they are approved by Parliament (headed by the PM) and signed by the GG.
By tradition, the GG is appointed by the PM. In theory the GG could refuse to sign a bill into law, but the PM could replace her with a new appointment, so the PM with the support of Parliament is the real authority.
The two are not mutually exclusive. A country can be a constitutional monarchy as well as a Parliamentary Democracy. Canada and Britain (and indeed, many countries in Europe) are both.
The only difference between the two is that in a constitutional monarchy there is a monarch to give Royal assent to any bill, while in a country which is not constitutional monarchy there may have someone else (as they have the president in India, over there, any legislation passed by the Parliament must be signed into law by the president).
It is really a distinction without a difference.