The Special is set before the drama but it is set at the same school with the same teachers and deals with the same problems.
Both shows follow caring teachers (who themselves have delinquent pasts) as they earnestly try to reform their disillusioned, delinquent students (yankees). Gokusen has more lighthearted fun and outrageous situations; Yankee Bokou ni Kaeru takes a much more serious approach and is based on a real school.