The main difference between any kind of slavery and transatlantic slavery was transatlantic slavery's racial aspect. The fact that a slave could be freed and still discriminated against and this discrimination did ultimately make the lives of their descendants worse, is what differentiates transatlantic slavery.

As for other differences, Anglo-Saxon/Carolingian slaves were either domestic slaves, rowing galley ships, or working on small farms in a moderate climate. Being a galley slave was a horrible existence and the slave probably did not live very long, however, it was possible for a domestic slave or a small farm slave to have a decent life.

Transatlantic slaves were working in many capacities but for the most part on plantations in a hot tropical climate. They worked longer hours and had shorter lifespans due to harshness of the working conditions and the demands of their masters to produce as much product as possible

Source: Davis, David Brion. Inhuman Bondage. The Rise and Fall of Slavery in the New World. Electronic Edition. Oxford and New York: Oxford University Press, 2006.