A friend asked me if I could find any information about reactions in Japanese to Utada Hikaru recently coming out as non-binary, and some of the sources I managed to find reminded me of this question from a while back.
One article that functions as a good explainer about LGBT topics with a gay lifestyle magazine editor consulted heavily as a source breaks down four types of セクシュアリティ:
【身体的性】からだの性。生まれながらに定められている性別
【性自認】こころの性。自分がどのような性を自認しているのか
【性表現】ふるまう性。自分が表現したい性
【性的指向】好きになる性。どのような性に恋愛感情や性的感情を抱くか
…
『トランスジェンダー』は生まれたときに割り当てられた性別が、自身の性自認（こころの性）または性表現（ふるまう性）とは異なることを指します」
So it uses からだの性 as a way to explain assigned gender, and こころの性 as a way to explain gender identity.
A lengthy post written by a non-binary person about it and negative or ignorant reactions seen online, has this this part in the midst of explaining ノンバイナリー:
ぼくは “女性” の身体を持って生まれたけれど、生まれてから一度も自分を “女性” だと思ったことはない。でも、だからといって “男性” になりたいと思ったこともない。
So there’s a similar construction there (but with scare quotes undercutting it a bit).
Not conclusive, by any means! But I thought it was interesting since I don’t remember any of us coming to any kind of conclusion (and I’ve felt a little weird about it in manga recap pages too).
My impression from this is that it’s a messy area like it is in English, but I think the 体/心 pair might fit at least a bit better (and less offensively) than body/mind does in English (or at least be an even more tempting easy way to explain it), because they’re more of a direct paired set, and because of the extra connotations of 心. Like, mind+heart+core+self vs. body, feels a bit better as a distinction to me than just “their body’s X but they think they’re Y” for example.
I presume also though of course, that in pieces where they didn’t feel like they had to explain these concepts to a general audience, using phrases like 生まれたときに割り当てられた性別, 性自認 and 性表現 without using 体/心 at all would be even more preferred.
Ultimately just speculating based on limited sources though!