We had a panel of fathers at Grace Church give their thoughts on this question:
The key difference is the question "Why?" Why does your child hit another person? Usually, it is out of angry and self-centered motives, such as not getting his way or trying to get something that another child has. James 4 states that selfish desires lead to conflicts, and this behavior is equivalent to murder. No one ought to ever hit or attempt to hurt another out of anger or selfishness.
On the other hand, a parent must never spank a child in anger. Discipline must always be an act of love and care for your child (Proverbs 3:12), not an act resulting from frustration or anger. Spanking in anger does not bring about God's righteousness (James 1:19-20).
During any form of discipline, including spankings, your child needs to know that you are acting as God's agent, out of love for him. Through discipline, you must model the same love that our Heavenly Father has for us (Hebrews 12:7-11).