I prefer Asperger's for my own situation. I admit that Asperger's is part of the Autism spectrum, but there are identifiable "sections" on the spectrum that differ somewhat from one another. Classic Autism is more severe. Asperger's is at the high end of the spectrum. My condition is in the Asperger's part of the spectrum. Unfortunately, most of the public think of Classic Autism when they hear about anyone on the spectrum. I sympathize with families dealing with that, but I prefer to have my condition accurately identified, when it's necessary to tell people about my at all. There is a definite difference. When I first heard about autism, it was a case of classic autism, and I never saw any resemblance between myself and the child involved. When I first heard about Asperger's, I immediately saw myself in the article. Further research only reinforced that. Outside input from other people who had read about Asperger's and believed it fit me, served to confirm my belief in my having it. I have continued to research this over the years, and it fits me. I also have a few of the co-morbids, but fortunately, not all of them. Since I fit very much in the Asperger's part of the spectrum, I will stick with referring to myself that way.
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If a man does not keep pace with his companions, perhaps it is because he hears a different drummer.
Let him step to the music which he hears, however measured, or far away.--Henry David Thoreau