Actually, the Spanish enslaved the American Indians, in the Carribean and New Mexico.
The New Mexican pueblo dwellers revolted and killed their enslavers.
There is some evidence that in addition to black slaves who came to St Augistine on the very first boat, there were indian slaves as well.
The Spanish were forbidden by the Pope and their king to enslave the Indians. Does this mean independent Spanish expeditions did not enslave Indians? Of course not - Madrid was far away.
But slavers were punished. Columbus himself was actually imprisoned by the Spanish government for having sold Caribbean natives into slavery.
The black slaves were sold in Spain by the Muslim slave traders, who were also the ones who revived the practice among the British. However, slavery in Spain was more like indentured servitude: a slave had to be free to receive religious instruction and be baptized, marry (and then he could only be sold with his family), own property, and buy his own freedom or be manumitted upon the death of his owner.
By contrast, the British colonists in Georgia and SC not only forbade all of these things (baptism, marriage, buying of freedom), but at various points their law provided for the death penalty for people who gave religious instruction to slaves.
There was a big difference, which is the reason that Latin America has a mestizo population and the US does not.