Yes, they are two very different games.
Skeet is shot on a field with two trap houses, on a semicircular field. Targets are thrown over a central stake and do not vary from the flight path. Shooters progress around the skeet field over eight stations. It entails both single and double targets. Skeet was developed to provide hunters with targets at various angles normally encountered in the field. The targets are close and open chokes are used.
Trap is shot on a field with five shooting stations with a single traphouse throwing targets away from the shooters. The targets vary in height and angle going away from the traphouse. Originally trap derived from a live bird game, it is the oldest of the disciplines. Trap is usually shot with tight chokes. Trap has several variations including a doubles game and a handicap game that moves shooters farther from the Trap house as their shooting ability improves.
An excellent book on the different games is "The Clay Target Handbook" by Jerry Meyer. It explains the games in detail as well as giving the rules and variations.
Geoff Ross