In DSM-IV, there are five different autism spectrum diagnoses. Two of them are 'autistic disorder' and 'Asperger's disorder'.
Autistic disorder requires three sets of symptoms, in social, communication and repetitive behavior. It makes no requirements for functioning level, so people meeting criteria for this diagnosis can range from odd but mostly functional to nonverbal and severely disabled. The higher end of this is 'high functioning autism'.
Asperger disorder requires the exact same social and repetitive behavior criteria, but doesn't require any communication problems, and indicates that the person has to have roughly normal development apart from the specific difficulty in social skills. So, no speech delay, no serious delay in self-care skills. Plus, you have to not meet criteria for autistic disorder.
Problems arise with this distinction, though.
Problem 1: Many clinicians ignore part of the criteria. For example, a kid with NVLD who has no speech delays but has social impairment could be readily diagnosed as Asperger's disorder. Problem is, some of those kids also have motor and self-care delays - it's possible, for example, to have a kid with a normal or gifted IQ who said his first words at 12 months but couldn't dress himself until he was 8. Technically, this kid wouldn't qualify for AS, because of significant self-care delays, but not many clinicians will diagnose autism in a kid like that. Many clinicians define AS as 'autism with no language delay' or as 'high functioning autistic who is sociable and has motor clumsiness' or some such definition. And each clinician uses their own criteria.
Problem 2: When researchers decided to look more closely at the DSM-IV criteria, they realized that they actually don't make sense. All people who meet the social criteria of autism actually meet the communication criteria as well, because those criteria can be met simply by having trouble with the social use of language, which is one expression of social impairment. Since Asperger disorder can't be diagnosed when criteria for autistic disorder is met, this means DSM-IV Asperger disorder does not exist.
This is why this distinction is being removed by DSM-V.
I do think meaningful subtypes can be described, beyond just functioning labels. But I don't see any use in calling one of those subtypes Asperger Syndrome/disorder. What Hans Asperger originally described was simply the higher end of the exact same syndrome Kanner described. The vast majority of people who now bear the diagnosis of Asperger Syndrome would not be considered autistic by either Asperger or Kanner. For that matter, many medium-to-low functioning autistics would not have been considered autistic in Kanner's time, either. (For example, anyone who had an early childhood regression, or has any interest in interaction whatsoever.)