It might be useful if you just read the posts and try and pick it up as you go along.
It's quite complicated, as you say, with all the acronyms and different strands.
I can help you out broadly.
There are two types of transwomen, according to Blanchards typology.
Homosexual transsexuals (HSTS) and autogynephiles (AGP)
Homosexual transsexuals are generally referred to as 'genuine transwomen'. They are attracted to men, usually have gender dysphoria which is a rejection of their masculinity and their male body, and are often fairly benign, just trying to get on with it under the radar.
They are often called Truscum by autogynephiles.
Autogynephiles (AGP) are different. They are aroused at the thought of themselves as a woman. It's a sexual fetish. And they are usually attracted to women. They are often late transitioners, are often married and have fathered children.
It's this second cohort who tend to be campaigning for access to women's spaces. They are 'male lesbians', the ones with a lady dick, or female penis, the 'transwomen are women', NoDebate. They are the ones who often say lesbians are transphobic for not dating them, and their penis. See cotton ceiling.
The other complication is this second, more aggressive cohort, are attracting just regular misogynistic men who want to dismantle women's boundaries.
TIM stands for trans identifying male. It's a banned term on mumsnet.
At least 85 percent of transwomen keep their male genitalia. They may take hormones to grow breasts and get a more curvy figure, but usually keep their penis (getting breasts, or shaving jawbones, etc, is still called sex reassignment surgery. It often has absolutely nothing to do with a penis). Of the two cohorts, it's the ones with gender dysphoria who tend to have the most invasive surgery. They would have felt female all their lives and are often effeminate. They 'pass' better.
The second cohort tend to transition late in life, after decades of cross dressing in secret.
They will often have used the narrative of the homosexual transsexuals to legitimise a fetish.
There is a schism in the community, with the first cohort trying to distance themselves from the second cohort, because cross dressing fetishists are giving men with gender dysphoria a 'bad name'.
TERF stands for trans exclusionary radical feminist. It's also a banned term here.
It was feminists who saw the misogyny in this ideology first, so that's why it was originally aimed at feminists. But it's now aimed at anyone who disagrees. Often followed by rape threats or die in a fire (DIAF). Men don't tend to get the threats anywhere near as much as the women do.
Gender critical women don't like the ideology for many reasons, but one of them is that reinforces damaging gender stereotypes.
Instead of a man saying I want to wear soft clothes, flick my hair, and act girly, he says in order to do those things he must be a woman. Thereby making those behaviours only things that women do.
It reinforces the gender boxes.
The gender recognition act was written in 2004 to make men able to legally become a woman. To help homosexual transsexuals navigate life easier. Also, at the time, same-sex marriage was illegal, and this was a good workaround. Become a woman, and you have a heterosexual marriage.
Coupled with that, the equalities act says that gender reassignment is a protected characteristic. Again, meant to help men with gender dysphoria.
It has been hijacked by AGPs who are exploiting it. It also means that men are beating women in sport, been transferred to female prisons, and all the other nonsense dreamt up by misogynists who exploit it at every turn.
I haven't mentioned women who identify as men, but that's going to have to be another post!