I wasn't even using terminology I was just describing it. Though AnsemSoD has canonically been called a being of heart or the longer "reduced to just a heart the being you call Ansem" which is in-game confirmation that hearts can exist as beings themselves. The secret reports also clearly describe the Kairi that flew into Sora as being Kairi's heart, specifically that Kairi's heart left its body then migrated to Sora. While Sora who is just a heart is said to have been returned to his human form. So saying Sora is a heart in human form, a being of heart, his body is a projection of his heart, etc... they are all correct ways to describe it. And honestly it's not much a mystery, the exact specifics aren't known and we don't have an official term for it but we know the general gist is the heart is just appearing in human form. And Vanitas shows us that it really is like a shell because give it enough beating and it will break.
I used terminology because I remember when it first appeared sorry. Ansem is a poor choice to use because he's also be described by Nomura and the games even up to DDD as a heartless as well. Meaning Ansem is either a heartless that's sentient, a heart thats taken on a shadowy figure or he's both and in between somewhere. Either way another clear fact of Ansem is that he got that way after going through the heartless procedure.
He admits it bluntly in KH1 reports that his form was an unexpected one:
Ansem Report 12 said:
I have transcended to an existence of only the heart. I should have come back as a Heartless, but there is no sign of such a transformation.
My body has surely perished. However, I am different from the other Heartless, keeping the memories of before, and I have not taken on the form of a Heartless. It is clear that there are still many things to be studied.
Ansem didn't expect to come back as he did and in this report alone refers to himself as both a heart yet a heartless unlike the rest. His form can be attributed to whatever middle state he returned in.
The Kairi part also doesn't debunk the part of her being visible to everyone or just Sora as before which goes back into my differences between her projection and Sora's body. Vanitas does indeed show a shell but his existence is also different.
My point wasn't to say they're incorrect ways of saying it but that there's no explained or truly defined way of saying it. Sora's body is different from the other examples meaning projected heart is indeed just a fan terminology, one of many mind you, to explain it. However it's also not exactly the same as the examples your giving.
The one closest to Sora in this category is Vanitas. Vanitas, while not a heartless himself, was forged from darkness similar to how heartless are and Sora was in a heartless form, which is his hearts darkness "made real", but turned human.
The more you think of it the more you realize Sora had something manifesting him rather than just his heart projecting an image of itself. So far all the projection examples were intangible to degrees while Sora was very physical in nature. He could've functioned perfectly fine as a human had Namine not messed with memories.
The Riku example is also vastly different because he's ghostly in the first appearance but only, with difficulty, takes a form once he's in the Realm of Darkness which is a realm of which we know little in terms or properties. We only know heartless live there, KH is lost there and that hearts gather there.
Edit. Gotta go now, have to go to work. See you another day. o3o/