the pm is the political leader

Nah

PM is the guy that controls the civilians and Commons.

the queen is a celebratory leader with limited dictatorship like abilities

your talking about the prime minister right?

the prime minister has taken the place of the queen in the lives of uk citizens and the commonwealth

if he controls the citizens and gov, hes the political leader

not really

a single pm doesnt have executive power over all of the common wealth

maybe in the eyes of the uk

I think you mean monarchist powers.

but they still celebrate the queen

yeah, by queen I mean monarch

the crown

same thing

The Crown is Parliament

In Canada

Parliament gets its authority from the Queen.

And is thus referred to as the Crown.

ok, so in canada is the prime minister elected directly?

No

The PM is the leader of the party that is elected to office with the most seats.

And the Leader is elected by the members of the parties

is it like the uk where they are the head of the party?

so the pm is basically the head of parliament

Not always.

well not in a minority government, right?

As a Minority government can subvert his agenda and call non-confidence to give him the boot.

the pm represents the crown to the people generally speaking

The other parties can form a coalition and then call an election.

But yeah, the PM is the head of the party with the most seats.

And he can appoint people to offices.

so it is practically the same as the uk

As a majority he is defacto leader.

Our system is based on British Parliament.

Yes.

But the Queen holds more power here than there.

We have the Commons and the Senate.

The Senate is full of people appointed by PMs.

From the Commons.

And they never change until one resigns or dies.