Is there a difference between contract bridge and duplicate bridge? If so, is there a difference in the scoring?
Contract bridge is named because before each game of bridge is played, a round of bidding takes place to agree on the "contract" in which that game will be played. For example, 1NT (one no trumps), 3H (three hearts).
Duplicate bridge is the same game. It is generally played in a club setting where several pairs of bridge players meet. The hands are pre-dealt. At the end of each game the cards are replaced in their holders and passed to another table to be played. Hence the name "duplicate". Each table in the room will play the same hands, rotated around the room.
The added "bonus" of playing duplicate bridge in a club session is the possibility of earning masterpoints. Serious bridge players can work towards becoming a Bridge Master or even a Grand Master. For more information on masterpoints, see the English Bridge Union website http://www.ebu.co.uk/masterpoints or the American Contract Bridge League http://www.acbl.org/masterpoints-results/masterpoint-awards-chart/
