Does sleep apnea, or lack of sleep, make kids look like they have adhd, or does lack of sleep actually cause adhd?

Lack of sleep. Poor sleeping is a major cause of behavioral disturbance in children. If your child snores, and if the snoring is significant it should be evaluated. I have seen remarkable changes in behavior in children with obstructing tonsils and adenoids following surgery. I have seen children with problems such as bed wetting cured by improving their airway.
Both/either. It can cause mild-moderate adhd-like symptoms, but not severe ones. If the child has significant drops in oxygen to his brain nightly, true deficits in cognition & attention can result.
ADHD and sleep apnea. The diagnosis of adhd is based on observed symptoms outlined in the dsm 4 (see http://www.Cdc.Gov/ncbddd/adhd/diagnosis.Html). One exclusion criteria is that the symptoms are not due to another mental disorder. There is no exclusion for sleep deprivation or sleep apnea. Symptoms of sleep distrubance can be indistinguishable from adhd. Treating the sleep disorder will make the symptoms better.