yes, it would be like if you moved states, you can't (or shouldn't) have more than 1 license at the same time. when you get your license in canada, they take your us license and mail it back.
are you a us citizen (therefore visa exempt)? if so, you do not need your pr card to fly to canada. you can fly to canada with your passport (since you don't require a visa), and then can show either your pr card or landing paper (COPR) at the border to prove your pr status. technically, your passport should be enough to do that too, since once it's scanned your status will show up in the system.
If you are a us citizen, you do not need a pr travel document. that is specifically for people who require a visa to travel to canada and don't have their pr card.