ADHD does not belong on the autism spectrum, but I think ADHD and autism could be considered as being under the same umbrella as neurodevelopmental disorders. I think they should both be classed as PDDs (pervasive developmental disorders) with ADHD being on one spectrum and autism/ASD on another. And this is just my personal opinion, but I'm inclined to think that Asperger's really exists within the overlap between those two spectrums.
They share some of the same genetic factors, and have some similar traits and symptoms, and tend to run in the same families and tend to be comorbid...but if you look at the actual diagnostic criteria, the disorders are quite different.
And the patterns of brain development and neural connectivity seen in ADHD are different from autism. ADHD is more of a developmental delay, that generally follows typical patterns of brain development but takes longer for the brain to mature...which doesn't necessarily mean that a person with ADHD ends up with a "normal" NT brain, most don't. But some people do grow out of the disorder, in other words their symptoms become subclinical as they get older. Autism has a more atypical pattern of brain development...it's not just a delay in development, it's a different path of development.
People who are diagnosed with ADHD can be very different from each other...but not quite in the same way that autistic people can have widely varying symptoms. With ADHD, the core symptoms are pretty consistent, but whatever is comorbid to ADHD can influence it and change the presentation. Lots of people with ADHD have a comorbid ASD, or autistic traits...but there are also many people with ADHD who would definitely not be on the autism spectrum. ADHD almost always has something else comorbid to it, but comorbid ADHD/autism is going to look very different than comorbid ADHD and psychopathy, or comorbid ADHD/NPD.