Gravity is defined as an attractive force between objects based on their mass. The Earth has a greater mass than anything on the Earth, so it pulls them down toward its center. This force is at work on a roller coaster when it reaches the top of a hill and begins its decent back down toward the Earth. Without something to stop it --- such as brakes or the track taking it in another direction --- it will continue toward the center of the Earth.
Elastic forces are the stretching --- or tension --- or compression of a material. In the example of a roller coaster, the rider compresses the seat bottom and the safety bar compresses the rider's shoulders. The coaster's train also compresses the tracks. However, if a coaster's train were to go around a loop and pause at the top, both the track and the riders would experience the forces of elastic tension as gravity stretches the the car and the rider toward the ground.
Friction is a resistance force between two objects. The objects can be standing still or in motion; friction is acting in either instance. When a roller coaster's train is in the station while riders are boarding it is standing still, which means the force of friction is greater than any force that would be causing it to move. While out speeding around the tracks, the coaster is also experiencing friction, causing it to move slower than it could theoretically move. This is why each successive hill the coaster climbs is shorter than the last. Unless propelled by extra energy, the coaster loses momentum due to friction during the ride.
Controlled friction is still a resistance force between two objects, however this one is used at the will of the ride's operator. Riders would probably be as familiar with this force on a roller coaster as with the gravity pulling them down each hill on the ride as the controlled friction is demonstrated by the brakes at the end of the ride.