A transwoman is not just a man that likes wearing high heels.
The ongoing ignorance and misunderstanding from very many people - here and elsewhere - on these sorts of issues is somewhat worrying. As indeed is the casual or jocular way in which "people (not) like us" are being derided or dismissed...
As you rightly say, there are many men who like to present a visual image of themselves which is "traditionally" assigned to women. The celebrated British artist Grayson Perry is one such person. He likes to wear dresses, heels, makeup etc precisely because he wants to challenge arbitrary perceptions about what males and females "should" wear and look like. For most of his adult life, and especially given his high profile, he's had to endure a steady barrage of stupid and ignorant inferences about himself - most usually, of course, that he must be either gay or transexual (he is neither). And sadly, many of those mistaken inferences have been made by people who should know far better.
Other men like to wear "women's" clothing, makeup etc for other reasons, but without it signalling either their sexuality or their gender identity. Knuckleheads will however continue to either laugh at them, assume that they are mentally damaged in some way, or assume that they are either gay or transgender.
And as you say, transgender identity does not map 1:1 with adopting a visual personal appearance which is "traditionally" associated with the opposite sex or gender. Indeed, many transgender people wish to adopt androgynous appearances. And (as you say) many (eg) men who wear dresses and heels are not transgender.
It'd be helpful to any form of meaningful debate here if more people understood what transgender identity actually is, and what it is not. And it would also be helpful if they understood that the near-totality of transgender people not only do not lighty make the decision to identify as transgender: in fact, they agonise over choosing to identify as such. It seems to me that there are still people within this thread who appear to believe that identifying as transgender is either a) something which is frequently done on a whim or according to "woke" fashionability, or b) something which (eg) evil men might do nefariously in order to access women-only spaces, with the purpose of satisfying male heterosexual desires.