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.
