The tendentious arseholes who edit such topics at Wikipedia have a mass debate about this.
en.wikipedia.org/wiki/Wikipedia:Neutral_point_of_view/Noticeboard#Definition_of_%22trans_woman%22
Basically the proposer of the first definition argues the first definition is not only factually accurate but also relatively more neutral since there is neither settled debate nor public opinion on whether a transwoman is a woman.
The debate goes off into such tangents as whether a TW was 'AMAB' or is 'biologically male', as the 'AMAB' label itself is obviously massively disingenuous, as it was only originally intended to be used for intersex people, where there was some biological ambiguity. In the case of TW there is no such ambiguity, the 'TW' thing implies a difference between gender identity and fundamental biology.