Both correct.

You "preclear" from most (if not all?) Canadian cities at the foreign airport when you fly nonstop to the US. I believe you also preclear from several other countries (Iceland?, for example).

Once you preclear, you've basically entered the USA, and your flight is basically considered domestic at that point... so you'll also then have a TSA style checkpoint (removal of shoes, etc) to go through.

Also, domestic luggage allowances apply to your ticket (so it costs $$ for checked bags...)