What the Muslim slave trade focused on were women. The Europeans came across the Americas, and they begin to look elsewhere for a labor supply- this is when they drop down to Africa for slaves. For the 16th and most of the 17th century, the slave trade in Africa was dominated by Portugal. Ultimately, Portugal will lose its control of the trade, and then the British will replace their power in the 18th century. The actual process of getting their hands on these people, forcing them onto ships and taking them to the Americas involved two processes. One way was to actually construct slave trade forts. This had the virtues of having a place where you could physically lock up the slaves until they were shipped to the Americas. Europeans sometimes used a ship to shore method instead. Basically, you anchor a ship just off the coast of where you're doing business,, and you go back and forth in small trips. This had the virtue of allowing you to move your operation to wherever the business took you. African merchants were part of the slave trade business. In other places, government was involved in the slave trade process. What countries were involved? Well, the transatlantic slave trade was a west African phenomenon. The Asante Empire became a major player by taxing. Congo resisted because it didn't want to be involved in this ugly business. The kingdom of Dahomey also resisted, which didn't work either. The Europeans came in and made life miserable for your government and your people if you did not become involved. They tried to incentivize participation in the slave trade. They sold you certain European goods that you really wanted. This is the basis of triangular trade. Europeans had manufactured goods that they sold to Africa. One of these things was iron in bars, ready to be melted and shaped. The Europeans by this point had developed process that made iron in Europe cheaper. Rum was another. Distilled spirits was another. A lot of that came from the sugar in the Americas.
Tobacco was another product, and the biggie was guns. What came from the Americas was the sugar for the run, the cotton for the cloth, etc. Another reason- the Europeans went in and actively started conflict. What the Europeans did is lay on that.
Diaspora refers to the dispersal of people against their will. In the case we are talking about the African Diaspora.