There is something called the Autism Spectrum. This is a large bubble that they put children into who have specific traits: typically low ability for empathy or social skills, ocd traits or repetitive behaviors. Now the problem with the Autism Spectrum is that every child is unique and they can fall anywhere from being a functioning brain child (considered "high range or functioning") with no apparent social skills to a mute child unable to handle any changes or variations in his or her daily life (considered "low functioning"). Also many other genetic and environmental issues can act similar to Autism.
Pdd and aspergers are both TYPES of autism that fall in the higher range of the spectrum (Well I'm not sure about Pdd, but aspergers definitely does). So with your child what happened was at 2 they noticed specific traits unique to children who fall within the Autism spectrum. Because there are so many types, they didn't know what it would be classified under so they might have just said you're child is autistic. When he was 2, pdd was diagnosed- and personally I feel like this is just a temporary diagnosis until they can better qualify where your child is and what specific need he will have. However by 8, they had seen enough to be able to be confident that he definitely has aspergers.
Now as far as the genetic goes, as far as I'm aware they haven't linked any specific chromosome to autism although there is definitely a genetic connection somewhere. (My nephew and his father both have Aspergers.) Now they ruled out Fragile X syndrome which can be a misdiagnosis of someone within the lower functioning autism spectrum. Fragile X is also a productive mutation as one of the "arms" of the Chromosome X duplicates then gets "longer" with each generation until a fetus is no longer viable. So its possible that a small duplication on the X chromosome that could be considered Fragile X Syndrome and could have been the cause of your child's behaviors. However, that was ruled out so it's not. You don't have to worry about it.
Now a triplication chromosome 13 ptsktsktsk is telling you that on one of his chromosome 13 (everyone has 2 of each kind), a specific gene or allele mutated. In this case, if I'm reading it right he has 2 more tsk than he needs. Unfortunately, there is nothing that can be done about this, this is his DNA. Sometimes one good chromosome can pick up the slack of the malfunctioning one, or at least limit the effect. However, sometimes it's not enough and there is an issue. I'm not very familiar with your child's specific mutation but you might want to consider talking to a specialist. He or she will be able to let you know what to expect, what to look out for, and how to help your son live a happy life.