What is the difference between asperger syndrome and asperger disorder, or is there no difference?

None at all: These are synonymous terms. The "formal" diagnosis is asperger's disorder. Syndrome refers to a cluster of symptoms that co-occur and help us identify a disorder. All of this almost certainly will be changing in the next few years with the release of a new diagnostic manual. The proposal is to lump autism, asperger's disorder, and several others under the diagnosis of autism spectrum disorder.

No difference: They are the same and another term that is often used interchangeably is high functioning autism. That term as an official diagnosis is going to be fading from use as are some other autism spectrum terms. Most will be replaced with autism spectrum disorder and the level of functioning will be used as a descriptive term.