Would it be fair to describe the United States from 1877 to 1960 as an apartheid state? If not, what were the differences?

Let's start with a general introduction to the South African apartheid state of 1948-1991 which generated the name for an 'apartheid' system. If you have the time, you can take a look at Worden's excellent introduction to the general history of the country and its political system.

Broadly, the colony that would become the independent state of South Africa had a preexisting racial hierarchy based primarily on land ownership (and therefore economic power in an agrarian society). This skips over a significant chunk of the political interplay between the various colonial parts that would come together into South Africa. However, in order to maintain this power post independence, the white minority constructed a legal framework for "separateness" between the constituent races of country (White, Black, 'Mixed', and Indian). These laws and the culture enforced by them resulted in some very specific things that stand out: massive involuntary relocation of majority populations; the creation of defacto 'states' for the unwanted majority to stay in; and the systematic creation of a narrative regarding the history of the country to justify these moves.

The reason why I drew these three things out is because they serve as key points of comparison to look at the United States in the post Civil-War era. I'm relying heavily on the below text by Lassiter (which I've read most recently). There are plenty of sources that cover this material and even your question including Kushner's work. On the first point, while there was a significant amount of population movement in the US (particularly post 1910 - The Great Migration), it would be a reach to call this intentional and organized relocation of populations by the federal state. On the second point, there is no case where the US, or any of its constituent states created a fictional legal framework of sub-states or territories to corral and otherwise contain African Americans to a specific geographical area. On the third point; there was the creation of a myth to justify the history of the South, slavery and its role in the Civil War (e.g. "State's Rights") and the follow on Jim Crow-era petty segregation laws.

So, yes, there were a significant number of similarities between the two regimes. Petty apartheid laws were abundant; clear cultural distinctions were made between groups based solely on skin color; a narrative was constructed to justify these acts. On the other hand, the scale and scope of the legal actions taken by the minority white community on the majority black community were different and guided by the geographical reality and history of each country. In some ways, due to the preeminence of the US Federal Government and its dilution by Northern/Western states means that the apartheid structure in the US was vastly less centralized, much less systematic and much less obvious than in South Africa.

Sourcing:

Kushner, James A. Apartheid in America: An Historical & Legal Analysis of Contemporary Racial Segregation in the United States. Associated Faculty PressInc, 1980.

Lassiter, Matthew D., and Joseph Crespino, eds. The myth of Southern exceptionalism. Oxford University Press, 2009.

Worden, Nigel. "The making of modern South Africa: Conquest, segregation and apartheid." The English Historical Review 111.443 (1996): 1016-1018.