It's basically the same as how Drag Queens aren't trans. They aren't fully conforming to the idea of being a 'woman', just the fashion and expression of it. Many prominent drag figures use she/her pronouns while in drag but immediately switch back to he/him when out of drag.

Here are the Google definitions

Transgender - denoting or relating to a person whose gender identity does not correspond with the sex registered for them at birth.

Transvestite - a person who dresses in clothes primarily associated with the other sex (typically used of a man).

Crossdressing and/or drag is you like to be outwardly a woman/other gender. Trans is you ARE a woman. Full stop. Your meat suit just happens to not agree with it, thus the term gender dysphoria.

Note: I do not speak for a trans people. Nothing is black and white. This is just how I understand it best and figured it got the point across.

Maybe this will help?

Crossdressing and drag are related to gender expression. Cis and trans are terms relating to a person's gender identity and may or may not align with gender expression.

By no means am I an expert, especially on the intricacies of being trans and I don't want to cis-splain their experiences, but I do know that cross dressing has an overlap of necessity with them, but it's a ven-diagram/intersection rather than a circle.

People who are trans typically explain it as having always felt like they've always been in the wrong gendered-body. Wearing clothes that correspond to the gender they feel they are
(also, keep in mind MRI's have shown brain activity that more closely matches the gender they feel they are than the gender they were born with, as well) is way for them to try and reconcile the way they feel with the way they were born. It's usually an early stage in socially transitioning, whether they later choose to chemically/medically transition or not (and keep in mind, this is not always the end goal for people ... simply being acknowledged as the way they see themselves is enough for some people and they shouldn't be afraid to be in public because of that!).

People who cross dress on the other hand may be doing it because they're trans and feeling out the early stages OR ... just because. It could be the way a textile feels, it could be sexual, it could be non-sexual, it could be because they just like it, it could be because ... you see where I'm going with this? There are as many reasons that people cross dress as there t-shirt designs (I may be exaggerating a bit with that one, but you get my meaning, I think).

I know NOFX is problematic, but I feel like "I’m a Transvest‐Lite" explains it decently (for one particular person anyways!):

I'm not transgender, I'm a lazy crossdresser
Who thinks makeup is too much of an ordeal
I paint my toes and wear shiny tight clothes
Not for the look, but how it makes me feel
I don't need things just right, I'm a tranvest-lite
I only shave to do the Time Warp midnight Saturday
I'm done with self-pity, I don't have to feel shitty
'Cause I wanna look pretty, so I give it the old city College try
Don't get me wrong, I still wanna be a guy
Who sometimes likes to dress like a girl
(He sometimes likes to wear diamonds and pearls)
Don't think I don't know I'm not fooling anyone
(He's a cross between Adele and Charlie Chaplin)
You gotta know it's not just girls who just wanna have fun!

Also, the beginning of the song is about the shame felt early on about it and is generally about getting the courage to not give a flying fuck about what people think.

Hopefully I did a decent enough explanation without trampling on anyones lived experiences. The simple truth is that both groups of people have completely individualized experiences and it's a different journey for every single person.

I agree with your comment, and I don’t think you’re saying otherwise. But definitely important to note that a lot of LGBT+ folks start off on the wrong side because of how they were raised, religion, etc. and the internal trans/homophobia that causes.

That said, there are also though a sizeable number of LGBT+ “one of the good ones” who think their support of republicans will keep them from being targeted by the laws they want to introduce (it won’t. This case itself is proof of that.)

I think that’s the important lesson to learn here for anyone voting republican and being a part of the LGBT community. The people you are voting for will not let you be just because you’re voting for them.

How anybody takes someone like that seriously is beyond me

Or existing in society at all. Sometimes in those parts of the country the first question upon meeting someone is "what church do you go to".

He didn't have to become mayor.

But it's not just "an issue". We are talking about a demographic and their legal recognition. No I'm sorry but we cannot agree to disagree on something so fundamental as equal treatment of people.

It's not comparable gun control.

Disagreeing on policy is one thing; disagreeing on human rights is another. You cannot be a Republican and have respect for queer rights at the same time. It has to be a 100% deal-breaker.

How likely are those Democrats to get bullied to the point of suicide if their "secret" of being against increased gun control was to come out? Or to preemptively commit suicide in anticipation of the bullying they're going to receive?

This is not the same thing. Democrats are, generally speaking, flexible about a lot of their positions. It's how they wind up with problem members like Manchin and Sinema. The Republican party is very different.

Good luck trying to get the terminally online to understand the nuances and complexities of the human condition