I'm not Canadian. And though I do know that the common term is the metric system, having worked in Engineering and much more frequently used metric measurements over imperial measurements, I'm very familiar with IEE/ASTM SI 10, so I've always referred to metric measurements as a whole, as SI. But I don't know why Canadians write S.I., as SI actually stands for International System of Units, so it doesn't directly abbreviate into S.I.The Metric System is old (1795). Napoleon even banned it and called it stupid.
But it was renamed in 1960, though I have only seen Canadians say SI and on 4 continents I have lived or traveled to, everyday people say Metric.