Neo-liberalism (Neo-classical liberalism) relies upon our classical liberal institutions to create and maintain a minimal state. “Libertarianism” because of the efforts of the Rothbardians to appropriate the term, has become synonymous with anarcho capitalism. So, if we are using the word libertarian, we must separate the Libertarian party, from the libertarian sentiment, from the anarcho capitalist philosophy. They are three different things. The term “neo-liberalism” is in part an attempt by those people with libertarian sentiments and support for classical liberal institutions to differentiate themselves from ideological anarchists. The term ‘liberal’ has also been appropriated by socialists and democratic socialists. Classical liberal has an antique meaning. So neo-liberalism is an attempt to create a definition of contemporary economic and political knowledge (all five or six economic strategies) while maintaining a minimal state.
An interesting question.