Since nobody answered, I'll chip in. I've posted about Slavic slavery here. This is also a very complex topic because slavery was not some static phenomena that had specific rules. You are much better of seeking out a book on this because you are asking about differences in world slavery rather than something specific. What I can say about slavery is that our popular opinion of slavery is based most likely on American slavery in the South. The big difference is that this was institutionalized form of slavery, meaning it was systematic and generational. In other parts of the world, before institutionalized slavery, slavery was a part of human experience. Slaves were mostly debt holders, captured prisoners of war, criminals. Southern slavery was different, slaves from Africa were "domesticated" and were enslaved for generations. So if you had children, they were slaves. It was not like that in other parts of the world. Slaves could get their freedom by working their debt off and their children weren't slaves.

I can recommend these two books and they only touch slavery in Americas.

• Autobiography of a Slave

• The Comparative Histories of Slavery in Brazil, Cuba, and the United States

There are few works that try to tackle all the different forms of slavery, but here are a few that I recently posted on another question. Most only cover a few centuries and regions at a time.

• Patterson, Orlando. Slavery and Social Death: A Comparative Study. Cambridge, Mass: Harvard University Press, 1982.

• Berlin, Ira. Many Thousands Gone: The First Two Centuries of Slavery in North America. Cambridge, Mass: Belknap Press of Harvard University Press, 1998.

• Berlin, Ira. Generations of Captivity: A History of African-American Slaves. Cambridge, Mass: Belknap Press of Harvard University Press, 2003.

• Davis, David Brion. Inhuman Bondage: The Rise and Fall of Slavery in the New World. Oxford, England ; New York: Oxford University Press, 2006.