1) Natural Pureblood: The first kind, always existed, born out of the realm of darkness, they are actually "heartless" like Nobodies. They are nothing but darkness made real, that's all. They were summoned by MX to fight Ven in BBS>
2) New Pureblood: Produced when one gives into the darkness in his-her heart, the heart collapses into the realm of darkness, and the darkness within the heart manifests as a pureblood. Slaying the heartless does nothing, the heart must overcome its own darkness to return to light.
3) People-Emblem- Produced when an emblem attacks a human, the human's heart becomes encased in darkness, slaying the heartless frees the heart. This is actually seen in KH1.
4) Manufactory-Emblem-Produced by the Heartless Manufactory, I don't know how the Heartless Manufactory works.
The only thing I have unanswered is that what happens when a pureblood attacks a human, do they end up as pureblood?
Basically, I agree. There are two types of Heartless, Pureblood and Emblem, as we know, and those two types can be, in turn, born two separate ways.
For Purebloods, they are either born naturally in the realm of darkness or through the darkness affecting an individual in the realm of light/twilight. In the former case, my guess is that they are created from the darkness of the hearts that resonate with KH (even if KH itself is light, that is not to say it does not have darkness since it is, after all, surrounded by the stuff, and it certainly didn't get there out of nowhere).
For Emblems, they too can be born through the darkness affecting an individual like the Purebloods, or they can be created artificially via the Heartless Manufactory essentially infusing darkness into hearts.
Given that both can be created by the darkness affecting individual's heart, it's hard to say what makes an individual become an Emblem Heartless or what makes them become a Pureblood Heartless. I always thought that they'd become an Emblem Heartless if they're attacked and consumed by an
outside source of darkness (be it an Emblem/Pureblood, or some other dark creature), while Purebloods, in the case of an individual, are made when they are consumed by their own
internal darkness. Hence, it keeps in line with the concept that, no matter what, Emblem Heartless are unnatural (either created in a factory or forcibly in an individual who wouldn't normally have been consumed by darkness) and Purebloods are natural (either existing alongside KH in the dark realm or being born from the heart of an individual that has plunged themselves in their own darkness).
With that in mind, I think that the consequences of Xehanort's experiment allowed Heartless to proliferate.
Originally, when there were only Purebloods, my guess is that they were largely confined to the Dark Realm. By not only introducing them to the realm of light, but also creating the Emblem Heartless, Xehanort altered the very nature of the darkness of the Heartless. It became parasitic. Whereas before, the darkness could only be isolated in individual cases, now it can spread. Heartless can create more Heartless, and are consuming the realm of light.
I know what some of you may be thinking: Why, then, did Sora become a Shadow?
First of all, the Dark Keyblade unlocked the darkness of his own heart. It wasn't an external darkness that consumed him, it was his own. Hence, he became a pureblood.
And naturally, since the strength of the heartless is not based on the strength of the heart (like a Nobody is) but the strength of its
darkness, Sora produced a weak Pureblood, having little darkness in his heart.
Lastly, as for why Purebloods don't release hearts while Emblems do, that too, I believe, is dependent on the process of their creation.
For Purebloods, since the darkness is coming from the
inside going
out, it quite literally eats away at the heart. In other words, the heart is destroyed (and we know a heart can be destroyed, as we see with Vanitas), and there is no heart to liberate.
For Emblems, the darkness originates from the outside, but it doesn't go in... per se. Visualize it more as
surrounding, consuming the heart from the outside.
To provide some imagery, if the heart is an egg, and yolk is the darkness, the only way the darkness is coming out to create a Pureblood is through cracking the shell.
For emblems, the yolk of darkness (lol) comes from another source. While it may be attracted to the yolk of darkness inside the egg, the only thing this external yolk really does is douse the outside of the egg. It need not be cracked.