Being an actual, bona fide Astrophysics major and having taken more kinematics exams than I can remember without shuddering, the truth of the matter has finally been reached. Should anyone need a diagram of forces, I have about 20 different textbooks I could scan.
Roller coaster forces, and indeed the forces you experience in your car, are identical. A roller coaster designer's job is to push those forces to the point that you feel like you are out of control while really being under complete control.
This is an important point to remember when riding coasters, especially if they scare or frighten you. Mulholland Madness actually has the front wheels of the coaster significantly further back than normal so that the passenger car moves out past the edge of the track as it turns before actually beginning the turn. This simple trick gives a very convincing feeling of "Oh dear God we are coming off the track and we're going to die!!!"
Rotational kinematics (motion in curves) deals with 2 forces: Centripetal and inertial. Centripetal force is actually an acceleration (any change in speed or direction is an acceleration). Inertia is an object's resistance to acceleration. You feel this when you drive your car. Being pressed into your seat as you accelerate is actually your body wanting to stay still as the car tries to push it.
Imagine swinging a ball on a rope around your head. If you just throw a ball normally it's going to go in a single direction away from you. Attach a rope, however, and suddenly the ball goes into a curved path around you. The rope causes a centripetal force on the ball that pulls it towards you (the center around which it is orbiting). What keeps the string taut though is inertia. Newton showed the world that an object will try to keep doing what it is doing unless something acts on it. Without the centripetal force of the string, that ball would fly off in a straight line, so that is what the ball wants to do. In fact, at every instant as it flies around your head, that ball is attempting to fly off in a straight line, but the string keeps tugging in on it keeping it in a circle. Imagine yourself on a merry-go-round spinning fast and you'll know how the ball feels. As you spin faster, you feel pulled outward more and more. That is inertia trying to keep your body going in a straight line as the merry-go-round tugs you in a circle instead. You've also felt this in your car as you take a corner to tightly. Your body wants to keep going straight down the road like it was, but suddenly the car is turning sharply and you feel thrown to one side or the other. This is NOT centrifugal force as that does not exist. It is inertia countering centripetal force. The term "centrifugal" was coined by Newton in 1689 to describe the balance between centripetal force and inertia, it is not a force itself. The word centrifugal comes from the latin words for "center" and "to flee" and shows that it describes the tendency of an spinning object to obey it's inertia and flee, or move further, from the center around which it is rotating.
If you take a corner in your car at 5 miles per hour, you don't even feel that you are being "thrown" to one side because the centripetal force is significantly larger than your inertia. However, take a corner at 50 and your inertia is larger than the centripetal force and you start to slide across your seat. It is this delicate balance that thrill ride designers play with to make you feel like you are in a dangerous situation.