Yes, I do generally see a distinction between sex and gender — roughly, body and mind, or fact and perception — though I think that distinction tends to collapse in some places, and exactly where it collapses for each individual can be unique to them.

For example, based in part on our bodies, strangers may assume we're men or women—that's a sex-related aspect of gender.

Or, based in part on our feelings and how we live, we may classify ourselves (or be classified) as males or females—that's a gender-related version of sex.

Body/mind are intertwined, that's all. They just don't quite pull apart cleanly in the long haul. Sometimes that M/F column on documents is labeled "sex," sometimes "gender," and I never know which it's meant to be.

I think that's one of the interesting things about the term "sex assigned at birth" — it's talking about human perception of our biology and what we make of that perceived biology. It's like a hybrid term, talking about how our physical sex gets gendered and thus how we are sexed/gendered.

The term "gender confirmation surgery" never appealed to me personally. After all, if the surgery has no impact on my gender, what am I confirming for myself? Or for others? The term "sex reassignment" has similar limitations. i.e., yes, I want to reassign my legal sex, but that's not the entire reason why I'm having the surgery, and I'm aware the surgery won't physically change my DNA, so in that sense it doesn't reassign my physical sex. None of these terms are perfect.

Probably the solution is just to name a specific surgery rather than to try to tie it to "gender" or "sex." There might be no need to explain our motive for a specific surgery. But then we may still need some way to speak euphemistically or briefly describe how multiple surgeries feel related to us (e.g., "gender confirmation surgeries" in the plural). We could say "gender surgeries" or "sex surgeries" but then we sound weird.

The word "surgery" alone often does the trick.

¯\_(ツ)_/¯