Do we need to carry any passport or picture ID when we get to the Canada side?
You always should carry a photo ID when leaving the ship. As for a passport - it depends on the tour. The round-trip train tour doesn't require it. They have an agreement with Canada that as long as you stay on the train while they switch the engines you are not entering Canada. I believe the tour which includes the bus requires you to have a passport.
This tour is another example of needing a passport while taking a cruise. Although a cruise to Alaska might be "closed loop", which doesn't require a passport for the cruise, it does require a passport for some of the tours in Canada.