Does America divide history into feudal society and capitalist society?

No, the United States has been a typical bourgeois society since its founding.

The American Civil War, ostensibly the capitalist North, defeated the feudal South. In fact, even the manor economy in the southern United States, which has maintained some customs in the medieval history of Europe, is actually a capitalist economy, especially a political organization model, and a bourgeois democracy without emperors and royal families.

The core of feudalism is the enfeoffment system, which is essentially different from the manor economic system of private land, employing farmers and using slaves.