I think that you are largely correct, Janie. Children are not diagnosed with "personality disorders", because a person's personality is not considered fully "formed" until they are of reasonably adult age. Whereas children are diagnosed with "developmental disorders" such as Asperger's and adults would seldom if ever be diagnosed such unless they exhibited fairly extreme symptoms. Also, a schizoid might seem fairly normal as a child, maybe a little shy, and not really exhibit many characteristics till late adolescence or early adulthood.
There is in all practicality, considerable overlap, simply because psychiatric categories are not precise things. A lot of time and energy has gone into the writing of diagnostic manuals in order to clarify these categories but the manuals themselves emphasize that there are many variables and any given individual might have symptoms from several different categories. There is even a category for personality disorders that don't quite fit any of the other categories. A real "dustbin" category that... how would you like to be diagnosed; "Personality Disorder NOS" You wouldn't know exactly what you were... "Hi.. I'm disordered."
A person who was diagnosed as having Asperger's as a child would probably not be reclassified as a schizoid when they become an adult but would continue to be classified as Asperger's... even though their symptoms might be no different than a schizoid's. So it would largely depend on when one was diagnosed, I would think, but there are differences between psychiatrists especially about more subtle points and their own clinical experiences might have one favoring one diagnosis or the other.
Gary