So trans people might not have gender dysphoria, and gender dysphoric people might not be trans, is that what you are saying? (I'm not disagreeing, just trying to confirm).
The first statement yes. The second statement - it would be very unusual for someone to meet the criteria for a clinical diagnosis of gender dysphoria if they weren't trans, but yes it is possible.
There might be some overlap, but also people who will be one and not the other.
"Some overlap" definitely isn't an appropriate description. Gender dysphoria is the clinically significant distress that very often results as a consequence of being trans.
So it's important not to conflate the two, I would say.
Yes. It's important to recognise that the two things are separate.
I'm not sure what you mean by socially transition
Social transition refers to any action a person takes to live comfortably in their gender, e.g. changing name, pronouns, mode of appearance, participation in activities, etc.
how do agender people, for example, socially transition?
As above, they may change their name, pronouns, mode of appearance, etc.
Why would they need medical services?
I don't think this is a genuine question. As you well know, I'm sure, some trans people suffer from significant distress as a consequence of having physical characteristics that do not match their gender (e.g. having breasts but seeing self as being male). These individuals may seek out medical interventions such as hormonal therapies, and/ or surgical interventions, in order to support them to change these physical characteristics to alleviate that distress.
Or do you personally not class them as trans if they don't require medical services or need to transition?
No being trans is separate to whether someone social or medical transitions. Being trans is something one is, transitioning is something someone might do as a consequence of being trans.