The US runs what is referred to as a presidential political system, where Canada runs a parliamentary system. This distinction refers to the differing relationships between executive, legislative, and judicial branches of government.
For example, executive legitimacy in the US is preserved through a series of checks and balances, whereas in Canada, we have cabinet solidarity, which means that the members of the Prime Minister's cabinet must always follow his decisions, and not to diverge.
The American President is elected in fixed terms and can veto a bill, where in Canada we elect a party and are given a leader from within that party. Our Prime Minister does not have a set term, because he has the power to dissolve parliament, but alone, he does not have the same veto as a president.
For the most part, the difference are fairly subtle. We could argue that parliamentary systems might be able to pass legislation quicker than presidential systems, which would be beneficial in an emergency situation. It might also be fair to say that the American system is very secure, through a strict measure of checks and balances.
There's alot more we could say about this, but these are a few key differences between the two without going into a full-blown history lesson.