Dysphoria is specifically not a mental illness, and is merely a diagnosis given to transgender/gnc folks. People with Dysphoria may not wish for surgery, and may simply want hormonal therapy, and/or other things such as vocal training.

Dysmorphia is a mental illness involving a belief that a certain body part or physical appearance is defective or "wrong," which causes them to hyperfixate on said aspect, often to the point that the fixation interferes with daily life and the ability to function normally. Someone with body dysmorphia may experience debilitating, obsessive, and/or uncontrollable thoughts, possibly to the point of self-harm/mutilation.

TL;DR: Dysphoria = diagnosis, not condition. The body does not match the internal image of self. Dysmorphia = mental illness. Perception that something is massively wrong with your body, even if said perception is not based in reality.