These two terms are often interchanged. Discipline really means "to teach" or "correct". Christ had 12 men who were His disciples - He taught them. Discipline has a positive reaction to an inappropriate action. For example: a son is found out to be cheating on his test. Discipline would be: 1. To find out why, 2. Give him some good study guides, 3. provide him with the proper tools and atmosphere to study, and 4. to encourge him. 5. Give him goals to acheive, and 6. Provide rewards for his achievements - either verbal or physical.
Punishment is a permanent act for committing the deed. Using the same example of a son caught cheating on a test: 1. You "chew" him out, 2. tell him what a lousy son he is, 3. ground him,4. take away priviledges that the "crime" doesn't merit. The down side for the parent is, it takes more time to discipline than to punish.