you are the one using the terms colloquially. americans might use the terms conservative and liberal to represent republican voters and democrat voters respectively, but both of those ideologies are different flavors of liberalism as the rest of the world understands it.
since we’re unironically using wikipedia as a source for some reason, you’re conflating liberalism (https://en.wikipedia.org/wiki/Liberalism) with social liberalism (https://en.wikipedia.org/wiki/Social_liberalism).
you are the one using the terms colloquially. americans might use the terms conservative and liberal to represent republican voters and democrat voters respectively, but both of those ideologies are different flavors of liberalism as the rest of the world understands it.