“Why does the University of Washington consistently have higher global rankings than its national ranking”
Most likely due to different methodologies being used by different rankings. As one example, many US rankings use the size of the endowment and the percentage of applicants who are accepted as important ranking criteria. However, many schools outside of the US have significant government funding which does not allow them to pile up huge endowments without spending a significant part of this on improving education. Also, US schools use methods (such as rampant advertising to high school students, and unpredictable admissions policies) to encourage many applicants who are not likely to get in, whereas many schools outside the US are constrained by some combination of common sense, fairness, and government restrictions to have comprehensible admissions policies. This in turn can increase the percentage of applicants who are admitted by encouraging only those students to apply who actually have a decent chance of getting in. As such the methodologies that are used inside the US to rank universities would not make much sense for international universities.
“I need to know how reputable UW is internationally in comparison with UBC (British Columbia), and make my decision based on that.”
This seems like a poor way to choose between universities.
UBC and UW are both very good schools. You can do very well and get a very good education at either of them. A degree from either of them will be recognized quite widely.
Probably the first two things for you to look at: What programs does each school have in the area that you want to study? Also, which one is going to cost you more, and will either require you to take on debt? Which country you want to study in might be a reasonable third thing to think about.
One minor point: If you get a degree from UW, it does not come with a work permit. Instead you will be expected to return to your country of origin (whatever that is). If you get a degree from UBC, at least based on recent Canadian law (I haven’t checked in a few months), this will allow you to apply for a work permit to work in Canada. Does this matter to you?
I will admit that these schools are closely enough matched that I can understand why you are having trouble deciding. IMHO they are both very good choices (assuming that they have what you want to study and that you can afford either).