Classical liberalism was a naturalistic belief in market supremacy, understood to be a colossal failure by the middle of the 20th century. It was associated with the Gilded Age, which spawned the so-called Progressive Era, the ideological camps that followed, and the catastrophe that was the world wars.
Neoliberalism is what the capitalist class have insisted is a reformed liberalism, invincible to the problems that classical liberalism motivated. It is a far more centralized, 'managed' market supremacy without the naturalistic perspective. Neoliberalism claims to acknowledge that markets are not natural and must be tightly managed by experts.