I think you can describe the trans-atlantic slave system and its particularities compared to other forms of slavery with 3 related ideas: Race, Colonialism, and Capitalism

Race:

In the American colonies there were understood to be three distinct groups of people: White, Black, and Indian. The difference between the concept of race in the trans-atlantic world and previous ideas about the different types of people in the world were generally dealing with groups which lived in much greater proximity to one another and therefore had a much more similar complexion. So an ancient Greek might believe that the superiority of Greeks compared to other peoples justified the enslavement of non-Greeks, and might even believe that Greekness was an inherent birthright which could not be acquired by a non-Greek, but in practice the Greek and non-Greek have similar enough facial features and skin tone that it isn't really possible to tell if someone's parents were both Greek, or to tell if a person is or isn't Greek without talking to them.

However in America, the differences in complexion between people of European, African, and American origin were significant enough that a person's race could be identified immediately based upon their appearance. This makes it much easier to establish a racial caste system in which a person with dark skin can be assumed to be a slave. This means that even if a black person is released from slavery they and their children will be unable to integrate into the dominant culture.

The distinction between enslaved blacks and free whites made it much easier for the ruling class to maintain their power. The idea that the white elite and the poor whites were connected by whiteness helped discourage solidarity between the slaves and the poor whites.

It is important to note that the way race works in the USA was and is quite a bit different from most of Latin America, South Africa, etc. In the USA, the child of a black person and a white person was generally seen as being black and the child of a slave was the property of that slave's owner, regardless of the child's father. In many places it was common for white slave owning men to marry slave women, which resulted in mixed-race children becoming slaveowners themselves.

Colonialism:

The slaves were not being taking from their homes to the imperial core, they were taken from their homes to the third location of the colony. The institution of slavery arose in the colonies at the same time as other forms of involuntary servitude were being reformed in the mother countries of these colonies. Serfdom and feudal obligation was slowly being replaced with wage labor in western Europe. This presents a contradiction with the liberal enlightenment ideology which would eventually lead to the abolition of the slave trade by the British.

The tension between the colonial elite and the mother country is also an important factor in the mechanisms of slavery, but I won't try to explain that here.

Capitalism:

The institution of capitalism evolved alongside the colonization of America by Europe. Capitalism was possible because of the extraction of wealth from America and its concentration among the European elite. The plantation system required the hyper-exploitation of the labor of slaves to produce trade goods.

Conclusion:

The extreme cruelty and sustained exploitation of American slavery is unparalleled in world history.