There is a link between these two terms somehow, I think. I keep meeting people that don't fall under the criteria of Aspergers, but have signs of having neurological patterns similar to someone who does. People who have trouble walking in a straight line down the sidewalk when next to someone. People who have difficulty maintaining eye contact. People who respond a couple of beats too slow to social cues.
The reason I bring up Schizophrenia is not to imply that the people I described above are schizophrenic. But those habits are all clues to certain traits found in people with schizophrenia. It could be that to reach the degree of functional impairment known as schizophrenia, a person would need a certain amount/combination of these genes.
Asperger's Syndrome, I believe, is one specific collection of those types of genes. It modifies a person's personality in a certain way that is obvious to other people. But these traits fall over a wide spectrum, and not everybody with the problems of a person diagnosed as AS can be diagnosed as AS.