To nit the nit, Canada is a bicameral legislative system, but the upper house (Senate) is appointed rather than elected and is generally deferential to the House of Commons (though not always). Senators tend to sit for a long time and take a lead role in things like long term reports and recommendations from the civil service.
The Prime Minster and Cabinet hold executive power. The PM and individual ministers have far more power than the US president in some cases, less in others, especially with a very different set of powers delegated to the provinces. The Prime Minister controls the legislature itself and its agenda far more directly than the US President.
The Speaker of House role is very different and while it's an MP from the government, they are expected to be highly neutral in all matters (something the current speaker is struggling with).
The PM is not the head of state the way the US President is. That role is held by the Governor General, who has quite extreme theoretical power. In practice they defer to the sitting government in nearly all cases.