Both Aspergers and ADHD neurodevelopmental defects and they occur early in life and tend to have similar characteristics, but they are definitely different.
Some of their similarities are such as; talking nonstop, unable to pay attention on things that do not concern them, have difficult sitting still, having a hard time interacting with other people and also social awkwardness.
Some of the characters that occur in Aspergers and not common in ADHD are such as; children have a hard time understanding general rules, very high interest in one thing, difficulty in showing empathy, unable to make eye contact, difficult in understanding humor and also delay in development of motor skills.
Characteristics of ADHD that are different from Aspergers include;
Impatience, forget and get distracted easily, breaking rules although they understand them, unable to pay attention, engaging in physical activities that can easily hurt them.
People can have both disorders but its always important to consult with a doctor in order to rule out which disorder one has.