First, would you say there is a great difference between the term "core" as used by someone like say, Joseph Pilates, and the term "Dantien"? What would you say the major differences or similarities are?
I know very little about Pilates, but I believe the point is to have strong core muscles (lower back, abdomen, etc.) as a power base for all other movements. The point of the dantien (or rather one important point of, but let's not go there now) is that it's the natural control center of what Mike Sigman calls the suit and what Hunter described as a balloon animal. Developing the suit means tying your body together in a very specific and very physical way. It means that when doing e.g. Chen silk reeling you do not move that way because of choreography, but because you feel that's the way your body wants to move.
So the main difference between the term core and the term dantien is that they come form very different views of how the body moves.
One possible similarity I see is that they share the idea that the pelvic region of the human body is very important for generating power. The big difference however is what they do with that region and how they develop it. So focussing on the similarity would make to me even less sense than focussing on the similarities in leg usage and development between sprinters and marathoners.