That is exactly what this thread is about. I'm proposing a new term or concept, "bearing", to distinguish the feelings about body stuff, in isolation, from any kind of social identification.
I've been trying not to talk about myself any more because Swan is an asshole and I don't want to expose myself personally to that, but I feel like I am the best example I have of the way that those two things can come apart, and my own experience is the prime motivating factor I had to start thinking about this to begin with.
With regards to my physical body, I was born male, and haven't done anything explicitly to change that, though apparently somehow or another I seem to have rather feminine breasts. to the point that multiple people have commented on them, including someone once asking if they were real (all of them friendly, not taunting or anything). I never really thought I looked particularly femme for most of my life, though I wanted to, so those comments always made me feel good.
As for how I feel about that body, I don't have bad feelings about the maleness of it. I wouldn't call myself dysphoric. I feel positively good about some traditionally male, unfeminine things, like my height and strength. But I get good feelings at the thought of being more feminine, just physically, not talking about anything social yet. When I shave my face or body hair I feel better about my body. When I wear clothes that accentuate feminine curves (e.g. some shirts hide my breasts, some enhance them) I feel better about t my body. If I use one of those machine learning face-changing apps to see myself as a woman, I like what I see. If we lived in an immersive virtual reality embodied in lifelike avatars that we could customize to our liking, I would full time wear the body of myself-if-I-hadn't-had-a-Y-chromosome, but at my current height and strength, and with a penis for a clitoris. It's just cost and risk and quality and other pragmatic factors, combined with the lack of any particularly pressing unhappiness with my current body, that keep me from trying to approximate that in real life more than I do.
As for social identification, presentation, and role: I couldn't give a damn about pronouns. Most people gender me male and it doesn't bother me at all, it's normal and I don't think anything of it. Depending on how I'm presenting, people occasionally gender me female, and I feel a little like I've been complimented. I work from home and while there (so most of my time) I wear dresses or skirts. When I go outside I'm usually doing some kind of physical activity like hiking so I wear pants (men's, because pockets are useful), but often with women's shirts, but not always. I have long wavy hair all the time. I'm really busy and stressed so I'm lazy about shaving, just once or twice a week, but if I had the time I'd be clean-shaven all the time (and I wish I could just be hairless always without shaving).
So if someone asks me what my gender is... I don't have a straightforward answer with the terminology that we use now. To my ear as a native English speaker "man" and "woman" mean, descriptively, to most people, male and female, so I'm a "man" in that, yeah, I'm male, if that's what you're asking. But if you're asking how I want to be treated... I don't think men and women should be treated differently, so it doesn't matter, just be nice to me. Are you asking what pronouns you should use? I don't care, whatever feels natural to you, it doesn't mean anything to me and language ideally wouldn't compel us to gender people anyway. Are you asking what sex I'd like to be? Mostly female, but it's complicated (see above), and you're probably not really interested in that anyway. But that's the only aspect of "gender" that matters at all to me personally, so it'd be nice to have a way of talking about it, without implying anything about what pronouns you should use for me or anything else like that.