The Pacific Northwest is comprised of...

[Upper Canada Tory]

Pacific Northwest = Washington state, Oregon, Northern California

Alaska, Idaho, Montana, Wyoming = part of Northwestern United States

(Note: The Pacific Northwest is also a part of the Northwestern United States, but excludes Alaska, Idaho, Montana and Wyoming)

British Columbia = part of Western Canada

Yukon = part of Northern Canada

I basically consider the Pacific Northwest, Western Canada and Northern Canada three separate categories that are not interchangeable.

Also, I don't understand why places like Yukon, Idaho, Wyoming, etc. that don't border the Pacific are considered part of the Pacific Northwest.

[Upper Canada Tory]

BC is Pacific Northwest. Regions can include parts of more than one country.

They can, but it is best when regional classifications narrow down a location as much as possible. Most Americans simply don't think of a place such as BC or Yukon as being part of the PNW. I don't think even most Canadians do.

For example, if someone from Vancouver, British Columbia goes to the United States, and says 'I'm from the Pacific Northwest', will most people think of the possibility that the individual might from Vancouver?

More likely, most Americans will think someone who is from the Pacific Northwest might be from Seattle, Portland, Spokane, or somewhere else in Washington or Oregon. In fact, I think even most Canadians would think so if someone told them they are from the Pacific Northwest. The 'Pacific Northwest' label is misleading as it doesn't really narrow down the location much.

That's why I also exclude Alaska, Idaho, Wyoming, etc. from the Pacific Northwest and use the more general 'Northwestern United States' to refer to it.