The problem is that far too many people (especially in the US) don't understand the terms.
Liberalism (supporting the freedom of the individual’s personal life from government interference) is the opposite of authoritarianism (government control over individuals' personal lives). This deals with people, not businesses*.
Meanwhile left and right are positions on economics, that is, how much businesses (not people*) should be controlled. The furthest left is government-run, planned economy throughout (further left than socialism), while the furthest right is no control or regulations what-so-ever (while capitalism’s founding document, Wealth of Nations, argues for regulation of businesses).
Progressive, conservative and regressive are about how quickly and in what direction society should change for its own betterment.
Most people tend to conflate socialism, liberalism, and progressivism, and similarly conflate capitalism, authoritarianism, and conservatism.
A Libertarian is, in general, a capitalist liberal. So, yes, Libertarians are liberal, strictly speaking.
It can also be shown that many who decry actual liberalism are bigots rather than authoritarians.
