That’s a fundamental misunderstanding of political ideologies. These are all different ideologies from fascism. Although neoliberalism and by extension neoconservatism lead to fascism. No one is a classical liberal anymore. Compared to classical liberalism, neoliberalism is fundamentally its own ideology that was developed in the 20th century. Neoconservatism is a more conservative and usually more war hawkish version of neoliberalism.

Here’s a useful video about neoliberalism to improve your analysis.

https://www.youtube.com/watch?v=zswexNXorOE