And no, genderist ideology does not have "definitions" for these words. It has recursive statements like "anyone who identifies as a woman" or "whether you identity as a man, a woman or neither" which loop infinitely around the lack of definition at the centre with no resolution.
The only way to break the loop is to either tie it back eventually to physical sex and the fact that fundamentally we all know what a woman is really, or tie it to the gender stereotypes which have historically been assigned to female people. Both of those require a second definition of woman which is the actual, foundational definition without which the first cannot exist.
The reason genderists avoid giving them, trapping themselves in the never ending loop, is because neither foundation justifies the demand to treat trans women as if they were female. The first because to identify as a thing is not to be the thing and is therefore not a justification to be treated as if you were, and the second because it pops femaleness out of womanhood entirely, begging the question why should alignment with gender stereotypes be used as a justification to appropriate anything to do with sex.