Maybe the confusion comes from the terminology.
"Autism" is a synonym for "Pervasive Developmental Disorder". Both are names for the category of PDDs that includes Asperger's, classic autism, Rett's, CDD, and PDD-NOS.
"Autism" is also a synonym for "Classic Autism" or "Kanner Syndrome", which is a specific disorder within the category of pervasive developmental disorders.
"Pervasive Developmental Disorder" is a name for autism in general. But "PDD-NOS", or "Pervasive Developmental Disorder, Not Otherwise Specified," is a specific autism spectrum disorder. PDD-NOS is also known as "atypical autism".
So, if your diagnosis is PDD-NOS, you could correctly say:
"I have PDD-NOS."
"I have atypical autism."
"I have a PDD."
"I'm autistic."
The first two refer to the specific diagnosis; the second two refer to the general category. It is like saying, "I have a simple fracture of the right radius," versus, "I have a broken bone."
To add even more confusion, "Autism" can refer to both classic autism and autism in general. So, someone diagnosed with classic autism could say:
"I have Kanner's syndrome."
"I have classic autism."
"I have autistic disorder."
"I have a PDD."
"I'm autistic."
The first three in that case are the specific diagnosis; the last two are the general category.
The range of statements for Asperger's, in case you were wondering:
"I have Asperger Syndrome/Asperger Disorder."
"I have a PDD."
"I'm autistic."