How so? It seems to be a distinction without a difference.
Actually, sad to say, there's a world of difference.
A dysphoria basically just means you're really unhappy about something. A
dysphoria is basically like an
euphoria, except it's the polar opposite.
It can be
- about your gender,
- about your body shape (e.g., girls being unhappy that they don't look like a Barbie doll, or guys thinking there's something wrong with them if they don't look like Conan The Barbarian),
- about your body integrity (literally people wanting to be disabled; like, have perfectly good limbs amputated. And yes, not only it's real, but it's also a recognized condition in the DSM5)
- about your species (also not as rare as our friend would have you think: in fact we currently have a cat-girl pandemic of anime proportions

)
Etc.
Edit: fer fork's sake, even being unhappy while trying to quit smoking, i.e., nicotine withdrawal, can qualify as a dysphoria.
An estimated about 5% of the population has SOME dysphoria or another, and the gender dysphoria is one of the rarest. Meaning pretty much there are 1000 people with other dysphorias for every fellow with gender dysphoria.
And not only it's not a synonym for transgender identity, it only affects something like 1% of those identifying as transgender. Conversely, there are a LOT of people who qualify for that diagnostic, but don't actually identify as trans. They're just unhappy about being male or female, and may well wish they were the opposite or neither, but don't think that that actually makes them BE the opposite.
So, yeah, the whole "X is perfectly normal because the DSM-5 recognizes Y" shtick, is as BS as it sounds, when neither of the two sets actually includes the other. Syllogistic logic doesn't work like that.
But anyway, yes, there is a world of difference between the two.
And TBH, that it's managed to confuse otherwise intelligent bystanders into thinking that if you're talking about one, you're obviously talking about the other too, is just sad.