There are competing ideologies between the United States and the Rest of the World, essentially culminating in two approaches of diagnosing psychological and psychiatric health concerns.

One comes from the American Psychological Association, called the DSM and another comes from the World Health Organization called the ICD.

https://www.apa.org/monitor/2009/10/icd-dsm

This doesn't address the "dysphoria = trans" claim at all. As I wrote in the other comment, one can be uneasy or unhappy with one's body/gender without wanting to switch to "the other" gender. As a mathematician, it seems like people here are claiming {1,2} = R (real numbers) which is just weird, they're sets of different cardinality.

You are arguing semantics. The specific words that the scientific community uses to refer to reality in their models of reality often change.

For example, “discomfort” in gender dysphoria is a scientific term that implies a level of suffering on par with the “discomfort” one would feel immediately after a major surgery, during the recovery phase, except this discomfort is chronic.

Scientifically, people experiencing gender dysphoria are considered to be in a state of chronic suffering for which there is a medical treatment, called gender affirming care.

Not all gender affirming care results in gender reassignment.

I wouldn't think of it as an ideology. I mean, maybe it is, but it doesn't seem at all bizarre. I'm not really aware of the details, but I'd be hard-pressed to name a difference between the two. I don't (think I) have a position on the issue.

But trans means switching from one side of the binary to the other, while dysphoria means "unease or dissatisfaction" which is not at all the same. One can easily be uneasy or dissatisfied with one's perceived gender identity yet not want to switch to the other side of the binary. What about agender people, or people who just don't like gender at all?

I certainly remember as a teen being unhappy with the constraints gender put on me in social situations but that certainly doesn't mean I'm trans.

There is a semantic shift taking place in the scientific community regarding the use of the prefix trans when referring to sex (physical anatomy) reassignment as a treatment in gender affirmative care.

Unfortunately, politics keeps interfering with the word choices of scientists.