"Liberal" isn't only a word used for modern US/Canadian progressives. "Liberal" is used to mean someone who believes in "free-market" capitalism, free trade, private ownership of the means of production and anti-nationalizationism, anti-protectionism/anti-regulationism, and individualism/anti-collectivism. It's pretty much synonymous with right-wing "libertarian" ideologies, including neoliberalism, classical liberalism, and "anarcho"capitalism. This is what the word has always referred to normally, and is by far the most common usage in most of the world, and it's still used this way in the US – mainly in economic, philisophical, or "fundamental rights" contexts though.

Liberalism is pretty much the antithesis of socialism, in a purely left-versus-right sense at least. The American ideology is often considered "social liberalism" or even "modern American liberalism", which still holds beliefs of individualism and capitalism, but differs from liberalism in that it pushes for a regulated mixed economy, as well as the government contributing to fulfilling social needs like healthcare, education, and infrastructure. It also is defined by focusing on social justice/civil rights, as opposed to traditional liberalism (which is opposed to social justice and civil rights, believing people in a "free market" will decide to do the right thing). It ranges from being a centrist ideology to being a left-leaning right-wing ideology, so when the only opposition is basically dormant fascism, it is the "left" ideology. In a full political view though, it isn't leftism.

The American misappropriation of the term came from a time when the word "progressive" was starting to be seen as "radical" (and therefore negative). Progressives started using "liberal" instead, and it became a way to say "I only want some government intervention in the economy and social issues, but not a radical amount". When New Deal politicians like FDR popularized it, it kind of became cemented in American political discourse as meaning that.