I think that is the best way to think about it. Because if not, then gender dysphoria sounds mostly like it’s just about fashion.
I wouldn’t want to wake up and be a man, but not for any reasons that are biological. I work in a male dominated field, and most of my interactions are with men, I like the things I can do and get away with, where a man would not have the same experience. The male experience sounds lonely, tough, and a lot of your success seems to just depend on chance and grit. My life has some bad parts, but it’s softer and more comfortable. Would I have dysphoria as a man? I don’t know, to me it sounds like it’d be something closer to envy, but maybe that’s just dysphoria by another name. Maybe that’s the root cause of why so many men lash out at women.
It might be difficult to imagine how those two things are separable if one has lived their whole life with them in congruence. If perhaps, you close your eyes and concentrate on your being, there is a part of you that feels that your sense of manness of womanness is part of who you are? What would you do if you retained that sense, and woke up in the body of the opposite sex and were expected to behave in congruence with that contrary to your internal sense of self? It can be a bit like that.