Most people here have insightful answers to your question, viewed from a US perspective. As [email protected] pointed out, the notion of libertarianism is quite different between Europe and USA. It originated in Europe (i believe the first use was to criticize Proudhon’s misogyny, so a dispute between some of the first anarchists). It was then used as a synonym to anarchism, due to laws criminalizing anarchism.

Then some (relatively) anti-State american conservatives used the word for themselves, and successfully made it so that it now defines their philosophy rather than anarchism in US. In Europe (at least in France), both ideas coexist (here we have two words, libertaire for libertarian socialisms and libertarien for libertarian capitalism). As people pointed out, the main difference is seeing economical hierarchies as good or bad.

Nowadays in french, libertaire is not a strict synonym for anarchist, it’s rather a wide umbrella term to gather all anti-authoritarian leftist.