The US and Canada are not the same country. There was a World Cup final game in front of US fans in 1996.
You say it has to be called "Canada Cup" because it's only held in Canada (though it isn't).
The World Championships are (aside from 2008) only held in Europe.
If we called them the "North America Cup" instead of the World Cup, and the "European Championships" instead of the World Championships, at least we'd be precise.
An oft forgotten fact is that Canada and the US negotiated away the rights with Dr. Sabetzki to host an IIHF in return for their sanctioning of the Canada Cup and the allowance of professionals to participate at the IWHC.
http://www.iihf.com/iihf-home/history/the-iihf/epochs/1975-1989.html
"The long, tenacious negotiations between Dr. Sabetzki and the top officials of the professional ice hockey resulted in a solution which was satisfactory for both parties: the Canadians and the Americans were allowed to enhance their world championship teams with professional players; in order to be able to achieve that most effectively, the world championships should in future take place as late as possible thus ensuring that a suitable player selection from among the NHL teams eliminated from the Stanley Cup would be available.
In their turn, the Canadians and Americans undertook to participate regularly in the world championships.
In addition, they relinquished their application to host any world championship tournaments.
In return, a competition for the "Canada Cup" should be played every four years on North American territory with the participation of Canada, the United States and the four strongest European national teams according to the last preceding world championship with the understanding that all the teams would be allowed to use their NHL professional players."