The DSM-IV (the manual that psychiatrist use to diagnose ADHD) describes individuals with ADHD-PI as having many inattentive symptoms but fewer than 6 hyperactive symptoms. Essentially the DSM-IV describes the ADHD-PI type of ADHD as individuals who are inattentive but that are normally active.
People and kids who are inattentive and inactive have been described as having Sluggish Cognitive Tempo (SCT). The DSM III recognized this subtype of ADHD but it was done away with in the DSM-IV because of lack of research indicating that this type was significantly different from the 'garden variety' sub-type of ADHD-PI. In this recent study, people with SCT are referred to as individuals with ADD (This is an unfortunate acronym to use as that term has been used to describe people with ADHD-PI.)
The Michigan State researchers found, after careful analysis, that the group that they call ADD had slower processing speed than the individuals that they describe as ADHD-PI. The researchers conclude that this ADD subgroup is a distinct entity which is characterized by slow cognitive processing and no hyperactivity. It seems that this study has teased out the Sluggish Cognitive Tempo (SCT) group from the entire group of kids with ADHD-PI.
Studies such as this Michigan State study are essential because ADHD-PI at the moment is pretty poorly understood. Some psychiatrist and psychologist seem to see all individuals with ADHD-PI as having symptoms of SCT and others insist that the symptoms of ADHD-PI are essentially the same as the symptoms of the Combined type of ADHD (ADHD-C).
My guess is that before the publication of the DSM-V in 2013 more studies, such as this one, will be performed to tease out the differences in ADHD subtypes.
Processing Speed Weakness in Children and Adolescents with Non-Hyperactive but Inattentive ADHD (ADD). Goth-Owens TL, Martinez-Torteya C, Martel MM, Nigg JT.; Child Neuropsychol. 2010 Jun 16:1-15.; Psychology Department, Michigan State University.