Its ridiculous to suggest that neo-liberalism isn’t a direct philosophical extension of liberalism.

Neoliberalism just focuses on some specifics of liberalism like open markets and property rights, which were already things that traditional liberalism espoused. Its the defacto philosophy of the American body politic after WW2. Things like the IMF, the world bank, the UN, central banks like the federal reserve, the use of rates to manage economies; these are very neoliberal concepts and institutions.

I think its fine to interchange liberalism and neoliberalism in modern parlance, because they are basically indistinguishable as practiced.