Dr. Russell Barkley says hyperfocus goes with autism while perseveration goes with ADHD.
So what's the difference? Is Dr. Russell Barkley right?
I myself have never found evidence to suggest a difference between perseveration and hyperfocus when referring to ADHD. However, while 'hyperfocus' can be a psychiatric or non-psychiatric condition, perseveration is typically considered a psychiatric condition in all instances.
The wikipedia page for hyperfocus has an entire section dedicated to the confusion between hyperfocus and perseveration, particularly as it pertains to ADHD.
Hyperfocus may in some cases also be symptomatic of a psychiatric condition. In these cases it is more commonly and accurately referred to as perseveration (or perseverance) - the inability to, or impairment in, switching tasks or activities ("set shifting"), or desisting from mental or physical response repetition (gestures, words, thoughts) despite absence or cessation of a stimulus, and which is not excessive in terms of quantity but are apparently both functionless and involve a narrow range of behaviours, and are not better described as stereotypy (a highly repetitive idiosyncratic behaviour).
It is typical for individuals with ADHD to say they 1), can not focus on boring things and 2), can only focus on stimulating things, and that focus is often extreme. Thus it is both a concentration deficit and over-concentration, or generically: "hyperfocus.
Actually,if you saw a few of Dr. Barkley's presentations. He referred to people with autism spectrum disorder as hyperfocus because they focused immensely on fine details of their sensations and their environments. While this hyperfocus, lacks the big picture perception. For instance, the child with autism might focus on the car wheel, while not attending to the car itself.
While perseveration was well defined by the "upstairs" author.
EDIT: Scientists would agree that they have what the ADHD community defines hyperfocus, but some (not all) psychologist/psychiatrist would not appreciate the use of this term based on the definition alone. They would disagree on the word used to define it. They would agree that people with ADHD have perseveration, but not hyperfocus (based on the definition alone). There is science to backup issues related to perseveration. While positive aspects of perseveration is probably lacking in the literature (since that's harder to look for). Hyperfocus would be kept for the autistic symptoms of focusing far too much on one element or detail and not perceiving the remaining of the item for instance.
To make things more complicated, I know there is one psychiatrist who uses the term hyperfocus (although probably not in thescientific literature). His name is Edward Hallowell. He's more of a clinicians and a book writer than a scientist from what I remember.