typically infertile. The cases where reproduction has occurred, they had underdeveloped but not absent reproductive organs which were developed with some sort of hormone treatments to the point of being able to support a pregnancy
there's a lot to parse here but let me focus on the word "choice" first. being (legitimately) trans is NOT a choice - what you do about it is (within the same constraints as any other medical choice) . to your main point, IIRC "woman" isn't really a science term so much as female in terms of the physical biology. IMO, and this is not precisely an answer to your question, the failing of terminology here is that it has not yet evolved to the point that transsexuality is classified officially as a sort of intersex condition. They have come so far as to identify a physiological source, and to theorize an explanation for how it occurs that directly parallels the DSDs which result in intersex births, but there's a bit of political linguistic gamesmanship involved because intersex people (perhaps wisely) do not want to be burdened with the association with the politics of trans people. If you fold transsexuals into the larger subset of intersex people, then you somewhat clarify the medical distinction to male/female/intersex