I'm amused and somewhat disconcerted you find it complicated. It's really very simple.
We both know what "woman" and its plural "women" mean. We disagree about whether trans women (sometimes 'transwomen') are women, which we couldn't if we didn't agree as we do about those meanings. (It wouldn't make sense to say we disagreed: what would we be disagreeing about?)
So what is a trans woman (a transwoman)? Of course this question is related to the question, "What does "trans woman" ("transwoman") mean?" in that if you know what "transwoman" (I'll stop with the alternative; fill in if you like) means, you'll very likely be able to answer the question as to what a transwoman is.
Simple enough?
OK, so let's think about what a transwoman is. The word "transwoman" is something of a neologism (OED has 1994, which seems recent to me, don't know about you), so it's probably worth getting clear about at least a part of what it might mean (which will help us get to grips with the metaphysical question about what a transwoman is, as I said just above).
OK? Well, some people (often perhaps misled by the "woman" occurring in "transwoman") have wrongly thought a transwoman is a woman who is trans. But that's not the case at all. No, actually "transwoman" doesn't mean that: actually a transwoman is a man who is trans. Hmm. (I note that we don't need to know what it is to be trans (or what "trans" means) to know that about what a transwoman is.)
So there you go. A transwoman is a man.
You know what "woman" means, @DadJoke. And you know (don't you?) at least the relevant part of what "transwoman" means. (I just reminded you.) So you know full well about transwomen being men.
But you want to say transwomen are women. OK, say it. Just don't ask me to take you seriously when you do.
And, back where we came in: I'm sure you now realise talk of "us[ing] different meanings for the same word [sc "woman"]" was just a silly mistake on your part.
Oh, and one more thing. Notice I haven't talked about definitions. Ime, "definition" comes with too much baggage of various sorts. Nothing I have said depends on definitions of words. That's something you might think about too.
Mainly, though @DadJoke, you should think about stopping being so silly.