Sorry, I have been confused the past month about this topic. Tons of people have been telling me different things.
I'm pretty positive I completely understand it now though.
Pureblood Heartless are the darkness from someone's heart animated. When someone's heart is broken or unlocked, the darkness from within the heart comes out and turns into a Pureblood Heartless. Pureblood Heartless can also be created from a part of the darkness of someone's heart. For example, Riku made some of the darkness within his heart come out of his heart and it formed into AntiSora.
Emblem Heartless are created when someone's heart falls into darkness, whether it be intentional or forcefully. Emblem Heartless are hearts basically trapped inside of a shell of darkness. You can make your heart fall into darkness intentionally by allowing the darkness within your heart come out and take over your heart. The darkness wraps around your heart and you then become an Emblem Heartless. Your heart can forcefully fall into darkness by other Heartless or a strong amount of darkness taking over your heart. The darkness wraps around your heart and you then become an Emblem Heartless.
The difference between Purebloods and Emblems are pretty clear. Purebloods are the darkness from within a heart animated and "alive". Emblems are the actual heart itself consumed by darkness.
When Sora unlocked his heart with the Keyblade of heart, the darkness from within his heart came out and became a Shadow Heartless. His heart took refuge inside of Kairi. Unlike most Purebloods though, Sora's Heartless was aware of himself, which happened for unknown reasons; Sora is just special. When Kairi hugged Sora's Heartless, Sora's heart came out of Kairi and merged back with his darkness (Sora's Heartless) which made him whole again. (Not completely whole though, because his body, Roxas, still wasn't a part of him yet.)
Ansem, Seeker of Darkness is an Emblem Heartless. This is how Ansem, Seeker of Darkness came to be: Terra-Xehanort extracted his heart from his body. Unlocking a heart and extracting it are different. Unlocking the heart unlocks the darkness within it which turns into a Pureblood Heartless. Extracting the heart simply removed the heart from the body while keeping it completely intact, not losing any darkness. Terra-Xehanort did this and his heart put on a brown robe and was known as Ansem, Seeker of Darkness while Terra-Xehanort's body was left behind which formed into Xemnas. Ansem, Seeker of Darkness then took host of Riku so that he would be able to wield a Keyblade. In KH1, on the destroyed Destiny Islands, when you confront Riku controlled by Ansem Seeker of Darkness, he then willingly falls into darkness which turns him into an Emblem Heartless, which is the Ansem, Seeker of Darkness we all know and love.
All of this is correct, right?
If so, I have a couple questions.
If Emblem Heartless are created when someone's heart falls into darkness, then how come they didn't exist before Terra-Xehanort created that machine?
If Vanitas is the extracted darkness from within Ven's heart, then how come Vanitas isn't considered a Pureblood Heartless?