During the elementary school years, children's fights are mostly verbal. A bully however, makes an effort to intimidate, both verbally and physically.
There are specific characteristics of bullying that differ from the usual playground squabbles. A bully tends to be consistent: threats and physical aggression are recurrent and predictable. Also, a bully usually picks out a vulnerable victim and limits his or her aggression to that child.
It is very difficult for parents to admit that their child is a bully. But bullying is often symptomatic of deeper problems. The sooner parents recognize that their child is bullying, the quicker the child can be helped to overcome the behavior and address the underlying cause.
Since bullying normally happens when parents are not around, parents often learn about it from other parents, caretakers or teachers. Don't be defensive and don't blame the messenger. Talk with your child about the bullying, tell him it is not acceptable and establish consequences if the behavior occurs again. Supervise your child's activities closely to prevent any more incidents. Your concern is your child's well-being and the safety of other children, so your best move is to consult immediately with school officials and your pediatrician or other health care provider who can evaluate the situation and make informed recommendations.
Here are some additional articles and resources:
Article: "I Think My Child is a Bully. What Should I Do?" Education.com
Website: Stop Bullying Now, U.S. Dept. of Health & Human Services