The short answer: There is no difference. Officially, only ADHD exists. It comes in three varieties: ADHD predominantly hyperactive, ADHD predominantly inattentive, and ADHD mixed type. In other words, you don't need to be hyperactive in order to be diagnosed as ADHD.
The term ADD is merely a popular abbreviation frequently (mis)used to indicate that someone is inattentive and does not display symptoms of hyperactivity.
there is no difference between ADD and ADHD
ADAD, on the other hand...
Yep ADD is lack of concentration/ attention
Given that ADD and ADHD are not diseases of the brain, but rather, labels that are given to children and adults (for the latter, in many ways, being labeled with AD(H)D, or any other mental disorder (illness), serves as a form of psychiatric (moral) absolution of one's perceived failure, at some level, to flourish) are means of reifying those "inappropriate" behaviors-usually within one's social matrix, i.e., school, work, family. The addition of "hyperactivity", to date, has been "diagnosed" more in boys than in girls, which, to me, is strongly suggestive of the social contigency of the label. To date, there are no testable and falsifiable theory-model of ADD. What one is left with are any number of psychosocial and biological models to choose from, but nothing clearly pointing to a definitive biological (genetic) marker, although recent strides in the genetic sciences has led theorists to replace earlier "shotgun" theories with models offering greater explanatory precision. So, in essence, whatever theory one assimilates, the state of the science still leaves much to be desired, and one is left with his or her article of faith.
Here is a good article about the difference between ADD and ADHD: http://www.helpful-relationship-advice.com/symptoms-of-add.html
Hope it helps,
The folly of labeling problems in living and social conflict, as if such were indeed medical issues, has borne witness to the transformation of moral values into health values. There are now 300 plus discreet mental illnesses and disorders in the DSM, and although there might be some indication of revision in the ways and means of labeling psychosocial conflict in the individual, by and large, the medical model of explaining the former is well ensconsed in present-day culture. Cui bono?