The difference is that body dysmorphia is not relieved by achieving the desired body type. Gender dysphoria is. That’s why they’re viewed as different. The fact that they both are related to distress over a person’s body is irrelevant.

You directly implied earlier that I was describing body dysmorphia when I made the following comment:

"What about a guy who doesn't feel like he's a proper male unless he takes enough steroids to get "huge"?"

Under the definition which you just stated, that ^ doesn't classify as body dysmorphia, because many such people feel happy once they achieve the desired change. I have a number of cis friends who have gotten breast implants after being depressed over being flat chested their whole life, and they said that is completely addressed their issue. Likewise, I know a lot of scrawny guys with feminine frames who said that putting on a lot of muscle addressed their issues with their body. Neither of these classify as body dysmorphia under the referenced definition.

Experiencing dysphoria over sex-characteristics is a strongly defining characteristic of gender dysphoria in many pro trans states, which is why insurance companies are required to cover it, regardless of how the DSM defines it.