The first one has a simple definition:
Attention deficit disorder
The second one has a descriptive paragraph, as well as a discussion and links to additional resources.
ADHD is an acronym for Attention Deficit Hyperactivity Disorder. People with ADD and ADHD struggle to maintain focus on certain tasks as they have a more difficult time "tuning out" extra stimuli. They can become overly attentive to distractions most of us are able to tune out, be impulsive and over-active. Many children are "wiggly" and inattentive, but these children have these conditions outside the normal range for that child's particular age....
The adhd is more used and definitely more completely defined. In my anecdotal experience, ADHD is more commonly used in discussion among parents.
I'm somewhat reluctant to make them synonyms, since it's quite possible to have an attention deficit without associated hyperactivity and it isn't necessarily incorrect to tag a question with add instead of adhd. However, leaving them separate means it's easier to miss questions if you're looking for only one tag, and requires use of two tags if I'm asking a question that's relevant to either diagnosis.
I may also be overthinking this because I'm still learning/understanding the whole tags and synonyms thing :P