This is something that really isn't discussed nearly often enough, and it's also something the majority of medical professionals you might have to deal with aren't consciously aware of, but if we're specifically looking at gender through an explicitly medical lens? Hormones > All
Bigots are constantly putting out blatantly false information on this front, because they just really really desperately need gender to be some sort of rigid unchangeable thing and their response to reality constantly contradicting them is to just bury the truth in enough lies that they never have to look at it, and people who know better largely try to avoid putting too much stress on any of what I'm going to say past here, since another flavor of horrible bigot out there hyper-fixate on the medical end of things to do some weird messed up gatekeeping about who is and isn't "really trans" based on whatever standard they can find that let's them play the "oh no I'm real and valid, not like all those fakers you hate who really are lying or deluded," and screw those people too.
But if we're actually talking about real medical stuff that you want to be aware of purely for the sake of staying healthy and avoiding medical complicatons then... you should really seek out an actual medical professional with specialization, experience, and good discipline about staying up to date on all the latest studies, rather than getting all your information from some random woman on twitter who just reads a lot and has some relevant firsthand experience. But you know, for the sake of people who wouldn't even think to do that without hearing this from me first:
BASICALLY EVERYTHING which is different for men and women in the field of medicine (and also just like what your body looks/feels/smells/tastes/reacts like for that matter) comes down to either the relative levels of various hormones in your bloodstream or the way various other cells have responded (or failed to respond due to some rare condition) to those hormone levels. No really. Basically everything. Whatever it is you're thinking of that you think is some exception to that? It almost certainly isn't. As a general rule of thumb, all the really outwardly observable stuff is more a matter of long term exposure, because it can take a while for cells to shift gears, especially if it's something where a bunch have to move around or divide more or divide less or whatever to hit whatever target, years sometimes, and for actually medically relevant stuff, it's more what ratio of hormones are currently floating around and how does that interact with anything else?
Like... any time you have ever read anything about how messed up it is that basically all medical testing is done on men, and women have to just hope it works out for us too?
Please note that I, a trans woman who has been on HRT for years now, am saying "us" there, because yeah, ALL THOSE ARTICLES are talking about hormone balance stuff. The super sexist framing on it is that estrogens are way more complicated than androgens and harder to account for because testosterone is just so special that when you have a lot of it, it kinda shoves all the other hormones out of the picture and you don't have to worry about them interacting with whatever else you're throwing in the mix so much (please keep in mind too that I am both being super broad and vague and also paraphrasing sexist BS there, so huge grain of salt). When testosterone is relatively low though, and the whole gang of estradiol and progesterone and friends are riding relatively high those can interact in seriously different ways with other drugs and cause problems that weren't caught when they tested those drugs on dudes. And hey, guess what? If you're trans-feminine and on HRT, you are dropping your testosterone down even lower than it is for cis women, and cranking those relatively high ones in most women up to like, double or triple the cis average. So not only are you a woman as far as any of those drug interactions might go, you're like, a double woman. If there's a hormone based issue to worry about, you're WAY more likely to be dealing with it than like anybody else. And if you're taking testosterone supplements, again, that's getting boosted way over the average for cis men and suppressing other hormones more (GENERALLY! I seem to recall this being something where if you're self-medicating you can actually screw up and it's like an int overflowing in programming where your body goes "woah this is way too high, convert some of this extra T into E already!" so, endos are important) than tada, you're some kind of super man, medically speaking.
And you know, it's not just a drug thing. Do you know the symptoms to watch out for in terms of a heart attack? Are you sure you really do? Because, hey, the last time I went to a doctor, there was a big ol' poster on the wall listing heart attack symptoms for women, and even as someone who has known for some time it's a totally different list than the one for men, which is the list I guarantee you are familiar with, since for decades it was the only one anyone ever bothered to popularize, turns out I was actually really hazy on the specifics. Also turns out it was a perfect list of every single thing I had going on that one day at the gym where I ended up pushing myself way way too hard and almost passed out so uh... I really need to work way harder on my cardiovascular help and be careful about that in the future I guess. But also, again, as a trans woman on HRT, yeah turns out the women's symptoms are, in fact, the ones I personally should be more worried about (and I mean, do please note I'm saying "more worried about," because if ANYONE is showing the symptoms on EITHER list, that's bad, react appropriately).
And this keeps being the general rule of thumb as you go down the list. Any sort of potential neurochemical thing? Not only do those not care if you're cis or trans, people are always pointing at such studies when they feel the need to like medically prove that being trans is a real thing.
Anything that cares how thick or thin your blood is? Bleeding risks, or clotting risks, whatever? Yeah you start HRT, you're switching teams and becoming a star player. Think that's why the heart attack differences exist, even.
Skin thickness? Less likely to come up in a crisis, but yeah, HRT REALLY changes it. And casually it comes up a lot, too.
If you're starting HRT femme-wise, expect to see more random cuts and bruises and have a greater need for sweaters. It's a thing.
Really, the ONLY medical concerns I'm personally aware of where going on HRT WON'T switch how you should be counted are:
Your ability to get pregnant or get others pregnant (accidentally anyway, if it's something you're actively trying to do, ask your endo whether you should go off your HRT to help things along or what).
And LOSING the risk of cancer with regard to certain anatomical features. This being the closest medicine ever comes to having bigots side, they of course do a lot of misrepresentation and scaremongering here to make sure it's just as distorted as all the other public perceptions go, but, really this is pretty common sense. Women have a higher risk of breast cancer than men because you know, women kinda tend to have more breast mass for cancer to develop somewhere in than men do. Trans men who went through the wrong puberty also tend to end up with more cells to potentially become cancerous in that whole area than cis men, and if they don't get top surgery, those keep hanging out. The same thing applies to prostates/skene's glands, which is worth a little more emphasis because you don't tend to see or think about those, so trans masc types might not think about them growing nor trans femme types think about them not shrinking. And if you don't ever bother with any sort of surgery where your gonads get tossed in the medical waste bin, any sort of medical issue focused on those can obviously crop up still (I mean, it's possible that testicular/ovarian cancer rates drop with HRT since your whole reproductive system kinda gets orders to chill out and tone things down in general? And the rates kinda drop to zero if you get bottom surgery because again, the bin).
The practical upshot of all this is just that if you're trans just kinda err on the side of caution with the recommended frequency of shoving cameras up your butt and sticking your boobs in a big vice, assuming you can afford those little luxuries like preventative medicine via routine checkups.
Otherwise, as far as any doctor should be concerned, your effective gender should be whatever your hormone balance is most consistent with, and you should be aware that being trans is rare enough odds are good your doctor won't actually know that if you don't bring it up, so, do try to have that awkward conversation any time you're starting HRT or seeing someone new.
Also I apologize profusely to anyone who just read this thread and started freaking out. Not trying to make anyone paranoid and it's really not at all true that HRT makes you like, less healthy or more medically risky at all. In the most practical terms, it's quite the opposite, because any check-ins with anyone you might have in relation to how HRT is going can catch any health problems you otherwise wouldn't notice. For instance, I have some rare scary blood clot disorder I absolutely would never have learned I had if screening for it weren't part of my endo's pre-screening process. I get free updates on my blood sugar and such while checking hormone levels regularly. Just a general pattern of checking mirrors and other people's opinions on whether rad HRT changes are happening or not is a great way to spot anything worrying weird lump or mole wise (and extra incentive to be more healthy in general, fat only where I want it, toning muscles for where I don't, etc.) and that's before even getting into all of the staggering health benefits that HRT provides. The whole proper brain functioning and liking your own body and not dealing with the constant horror of dysphoria and all that are definitely going to outweigh, like, anything else you could ever think of.
And seriously, any sort of "trans cancer risk" anyone shrieks about is one or more of several massive lies. Don't worry