In simple terms

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ADHD stands for attention deficit hyperactivity disorder. It basically just means that the person has a really hard time paying attention to things or sitting still. It's mainly diagnosed in kids, but recently has started to be diagnosed in adults as well. Most people find it hard to pay attention to things that they don't find interesting, but people with ADHD can't pay attention to things they do find interesting, either. They're also "hyper" all the time, and will tend to talk fast and continuously, not be able to wait their turn for things, and move around a lot.

ADD stands for attention deficit disorder. It's the same as ADHD except without the "hyper" part. People have with ADD have a really hard time paying attention to anything, and get distracted really easily, like with ADHD. But unlike with ADHD, they don't have trouble sitting still, and they're not always moving around. They might seem more day-dreamy, rather than hyperactive.