Old vs new. Add was the designation for the disorder in the dsm-iiir, while the current (dsm-iv tr) & only approved designation is ad/hd, (enter subtype here). There are five designations: 1) adhd, predominantly hyperactive-impulsive type. 2) adhd, predominantly inattentive type. 3) adhd, combined type. 4) ad/hd persistent into adulthood. 5) ad/hd, not otherwise specified. http://www.ritalindeath.co.
Hyperactivity. Add is just a deficit in attention without hyperactive behavior. Adhd includes hyperactive behavior. The former is more common in girls.
New Vs newer. The next dsm (dsm-v) will probably call ad/hd something else, possibly "sluggish cognitive tempo.".