A world apart. On the surface at a social event, the two entities can look similar: poor eye contact, little discussion, odd utterances. However, a child with social anxiety will have normal social interaction in trusted environments, understand social cues, have a clear idea of social norms, adaptations, etc. A child with asperger's does not have these things, and has other issues like sensory and processing.
Asperger vs. Anxiety. Asperger show stereotyped behaviors, no reciprocity during social interactions, and show little empathy.
Big Differerence. Asperger syndrome is considered a developmental disorder. That means, one is born with it or it develops in infancy and early childhood. There are less effective treatment for developmental disorders. Anxiety disorders on the other hand, are quite common-affecting perhaps up to 25% of people during their lifetimes. There are great treatments for anxiety disorders, with many recovering completely.
Major. A child with social anxiety can learn to dial down anxiety w/ the right therapy (CBT (cognitive behavioral therapy) and /or medication-to remission. A child with asperger's lacks ability to recognize emotional/social cues and to be more pro social but this social awkardness is a lifelong cornerstone of the syndrome. Nonetheless behavioral therapies can make great strides in social function.