You can think of them as the equivalent of the DNC-preferred wing of the democrats

It does not and it's quite confusing. You'll often see people use the term LPC or Liberal and avoid lower-case liberal due to the confusion of that word. In Canada the Liberal party is a fiscally centrist/corporate & socially liberal(ish) (aka it's similar to the traditional British definition of Liberal). The Conservatives are a large right wing reactionary block that seems to be perpetually in the minority but with a large loyal voting block while the actual opposition mostly comes from three parties that rotate in and out of relevance as a left-wing voice BQ (Bloq-quebecois), NDP (New Democratic Party - fading since the death of Jack Layton), and the Greens (Environmental sorta, but also weirdly anti-science sometimes). And that's on the national level - at the provincial level it gets even weirder with the BCLiberals (recently named BCUP) being socially and fiscally conservative and opposed by the BC NDP and other minor parties.

Liberal doesn't mean the same as it does in the US because it barely has a consistent meaning up here.

In Canada, it just refers to the Power Corporation

No, I probably should have used "Liberal" to indicate I'm talking about the Liberal Party of Canada.

https://en.wikipedia.org/wiki/Liberal_Party_of_Canada

it's a bit of a misnomer imo. if we're talking about classical liberalism, the conservatives fit that label better. if we're talking about "liberals" i.e. the left, the NDP would fit that label better. the modern Liberals are more like neoliberal technocrats, who favour top-down state interventionism and who are the ones driving surveillance bills and attacking privacy.