I recommend against assuming this. It isn’t always true. The transgender and other gender-variant / gender-atypical community is not a solidly united and unified cluster of like-minded people and we do sometimes use terms differently.
I will answer for myself and perhaps make a stab towards generalizing about what other folks may mean, but when someone else replies you may see a different answer.
I identify as a male girl. (A gender invert, which I describe as a subtype of “genderqueer”).
When I was roughly in 1st and 2nd grade, I was identified by teachers, parents, and other adults as a well-behaved smart kid who was good in the classroom and could be trusted to be trying to be a good citizen. Most of the other people who were so identified happened to be girls. I considered myself to be in competition with the girls, whom I respected and admired and emulated but towards whom I had an initial attitude of “I will show you a boy can be as good as you”. So think of me at that age as the inverse of a tomboy. You could say “sissy” (I’ve used that term myself), but if you do, say it with pride.
By the middle of 3rd grade, other boys had made it really apparent that they didn’t exactly consider me to be defending the honor of the Boy’s Team in this competition. And I found them embarrassing. So a little bit at a time I shifted towards seeing myself as one of the girls. Not as female. I did not believe I was female (and I did know the difference). It was obvious to me that the more important aspect of “who I was” was that I was “like one of the girls (and definitely not like one of the other boys)”, and not what I had between my legs.
I was not the only one to whom this was obvious: the other boys pointed it out. They apparently didn’t consider this to be a complimentary observation. It was an observation that boys often made about other boys, sometimes in jest and sometimes as a serious critical observation, but the usual reaction was for the boy so accused to do stuff to prove it wasn’t so. I just said “so???”
After a couple years of this, it was totally true that who I was, to myself, was a boy who was not like other boys but instead was like a girl. I was proud of it and went to deliberate lengths to express it. If there had been a socially recognized identity in 1968 for “genderqueer gender invert, male girl”, I probably would have come out by 4th grade.
That’s me. I don’t use “gender” as another word for “sex”. My sex is and has always been male. I don’t think I “should have been female”, I don’t think I “am female inside”, or any other variant way of identifying as female. My gender, on the other hand, was “girl”, or “woman” — that’s an identity, the kind of person I am, where and how I fit in, how I think and historically have thought of myself.
Now for some people who are gender-atypical or gender-variant (or whatever term you choose here), their experience of this general type of thing, perhaps combined with specific feelings about their body itself (body qua body, in other words) leads them in a different direction: perhaps to think of themselves as “really female” despite having been “assigned male at birth”, and they may or may not seek hormonal or surgical interventions to make it easier for them to present as female. “Present as” has to do with how others perceive you, how they are likely to identify you. To bring it into alignment with how they identify to themselves.
Yet other people I’ve known have reacted yet differently to such experiences. I know a gay guy who talks about his childhood and coming out and coming of age (he has a stage act; talking about his sexual orientation is just a part of his routine and he makes it funny & clever etc). He talks about realizing at a young age that he was feminine, like girls and not like boys etc, and to him this is entirely coterminous with understanding himself to be gay. So… you’ve no doubt heard that sexual orientation and gender identity are two separate things, and indeed they are, and yet for some people they are not because they themselves do not experience them as two separate things. This is true for him.
It is also true for a vast number (probably overwhelming majority although who really knows?) of mainstreamish people who are either male masculine heterosexual guys identifying as boys or men or else female feminine heterosexual gals identifying as girls or women. For them they don’t see a reason to have separate terms for sex and gender, and until they first experienced the social presence of gay and lesbian people probably never saw any reason for a separate term for sexual orientation either, certainly didn’t need it for themselves, being male partly MEANT being attracted to feminine girls / being female likewise for being attracted to manly male folks etc.