Actually the British and Portuguese were the biggest traders with the Portuguese being the biggest then supplanted by the British
I'm not too knowledgeable on North American slave trade
@Akan @IllmaticDelta @Poitier mifgt be better able to touch on the specifics
I can say that the Spanish has little prescence in Africa due to many reasons, one being the Treaty of Tordesillas
But these charts indicate that Jamaica export a substantial amount of slaves to other colonies
So to answer your question slaves in the US were taken straight from Africa as well as bought from places in the Caribbean
To address your second question, whether the Spanish and Portuguese treated their slaves worse is a debate rhst differs based on the colonies in question and your perspective.
Many (mostly Latin) folks will claim Brazil and the Spanish Americas treated their slaves better the British and French because of the lack of sharp racial divides, manumission rates and interracial marriage in those places. The truth is in places like Cuba and Brazil it was more profitable to import a slave then keep him/her alive leading to high mortality, high amounts of importation, and numerous violent revolts while in a place like the thirteen colonies slaves were able to reproduce itself
DR is interesting because it didn't develop a large plantation style economy like neighboring islands so for most of its history it was full of poor whites AND slaves. Often these poor whites did the same work and had children with these slaves leading to a high free mixed population. Because of this many Dominicans argue that slavery wasn't so bad there.