Perhaps the best place to start is to recognize that Attention Deficit Disorder is specifically what it states: a difficulty with paying attention.
The person who has this condition has challenges in two specific areas: being able to focus/pay attention, and difficulties with impulse control.
Rather than just talk about A(ttention) D(eficit) D(isorder) versus A(ttention) D(eficit) H (yperacticivity) D(isorder), it would probably be better for me to tell you that there are three main subtypes of Attention Deficit Hyperactivity Disorder.
Type 1: Predominantly Inattentive The behaviors and traits listed below are hallmarks of this type:

• Becoming bored with a task after only a few minutes, unless it's something s/he is really interested in
• Difficulty focusing attention on organizing/completing a task or learning something new
• Trouble turning in homework assignments, or paying attention long enough to finish homework.
  
• Tendency to lose things (assignments, toys, pencils) that are needed in order to complete tasks
• Seemingly spacing out
• Difficulty processing information as quickly and accurately as others
• Difficulty following instructions

Type 2: Predominantly Hyperactive-Impulsive A child with this cluster of behaviors or traits will appear with the following:

• Constantly touching anything and everything around him or her
• Talking all the time, non-stop
• Difficulty sitting still for any period of time
• Very impatient
• Having a difficult time waiting for their turn
• May say or do things that get themselves in trouble.
  As a parent or teacher, you may be pulling your hair out, thinking, "How many times do I have to tell you this over and over, and you still do the same things over and over!"

Type 3: A combination of the above.
This is a brief summary of the differences between ADD and ADHD.
Did I miss anything?Let me know!