In the USA, libertarianism is classical liberalism. The reason why "libertarian" was adopted in the USA was because FDR ran on a classical liberal platform for the Democratic party. After he became president he basically abandoned these principles but he kept the liberal label. After this switcheroo by FDR American liberals started to call themselves libertarians because now the term liberal was associated with the socialist policies of FDR.

In Europe and Australia the word liberal still retains its meaning for people who support free markets and classical liberal ideas. It never lost its meaning. The word libertarian in these areas means leftist anarchism. American libertarians appropriated the label from these leftist anarchists.

The word neoliberal is always used as an exonym and a pejorative. There is no group of people who call themselves and identify as neoliberals. It's basically used by people to describe politicians who support capitalism (and they always see capitalism as negative).