Hi, NLD adult here.
Asperger Syndrome is an autism spectrum disorder while nonverbal learning disorder is just what it is--a learning disability affecting your right brain hemisphere.
People who have NLD have difficulty interpreting visual information, facial expressions, voice tone, sarcasm, jokes, have difficulty keeping track of conversations, fine motor difficulties. The thing with NLD is that we are affected by academics. If someone has NLD, then math is a great difficulty for that person. I personally can't organize mathematical concepts with my working memory very well and it takes me longer to learn that sorta thing but my reasoning is intact.
Here's another tibit: 80% of people with NLD also meet the criteria for AS while 80% of people with AS might not meet the criteria for NLD.
Some people do have both: I knew a girl with AS but she also had a dx of NLD due to her difficulties in math.
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Officially diagnosed with nonverbal learning disability, social anxiety disorder, and dsythymic disorder.