Autism & Aspergers Syndrome are similar only because they are on the Autism Spectrum. The Autism Spectrum is a long spectrum and ranges from very low functioning severely Autistic, to Asperger's Syndrome (high functioning). People who have Asperger's Syndrome (like myself) are very social & communicative. When you are on the low end of the spectrum, you don't speak or communicate with others. It all depends on degree of impairment and where the individual in the family comes from, and if they are taught independent living skills, ie, shown how to do things, like grocery shopping, household duties, and paying the bills.
But to answer your question Asperger's Syndrome is an Autism Spectrum Disorder, and yes it's part of and relates to Autism itself.
I trust this information helps you!