Yes, people with Asperger's are autistic.

As Callista said, Asperger's is a name for a variant of autism where there's no speech or developmental delay.

Basically, autism is a spectrum disorder - hence the term Autistic Spectrum Disorder. Asperger's is on the milder end of the spectrum. However, not everyone who's autistic have Asperger's.

Anyways, all this confusion regarding names are going to be removed soon because Asperger's is going to be thrown out the books and everyone is going to be labelled under "Autistic Spectrum Disorder".