Fair related, right?

This came up last week when my science module involved centripetal force...now, when I first read it, I thought I had just been mishearing people and thinking they were saying "centrifugal". Then as I read further, the author proceeded to say that centrifugal force doesn't exist, and all that you're feeling is Newton's First Law of Motion in action... ok, I thought, so I have been hearing centrifugal force, but like the book said, people are getting it mixed up.
So, when my mom graded my science study guide, she was surprised to read that. Apparently, when she was in school they taught all about centrifugal force, so I guess this idea is somewhat new. Then she asked what I was wondering about as well, "how do the rides at the fair work, the ones that supposedly work with centrifugal force?" Since I was having trouble understanding my science book anyway, I decided to do some online research, and see if I could find something that made more sense. I found quite a few things, and apparently it's quite a debated subject! I found several boards with people arguing that "how can you tell someone that centrifugal force doesn't exist, when they can feel themselves being flattened against the wall?" I'm still not altogether sure what exactly is true, but I found one website here that finally made some sense (if they're right). According to them, centrifugal force is the absence of centripetal force, and the object or person being forced against the wall is feeling 'centrifugal' force, but what's pushing them into the wall is 'centripetal' force. Now, if they're right, that makes sense to me. Here's their explanation of centripetal force.
And here's an article that explains how all this works in relation to the amusement park/fair ride, this is a report on a ride that malfunctioned, but it doesn't sound like even then there were too many injuries, and it's dated '95, and in eleven years I'm sure safety inspections have improved.
In the end, I'm not sure if it's just that they renamed the force, because to be exactly accurate centripetal means "center-seeking", while centrifugal means "center fleeing". It may be the exact same thing that my mom learned about in school, but since then they've discovered they were calling it the wrong thing? So I'm still not really sure what's true! That's one thing I'm finding in my science book, I find Physics (and this is only simple Physics) very hard to understand, but fascinating! If anyone know what really is true about centripetal v. centrifugal, please let me know!

And now, for something completely different: I just opened a new tube of toothpaste, and it's slippery toothpaste. And I really don't like slippery toothpaste, the toothpaste with baking soda in it is best, because it had a bit of grit to it(without feeling like sand), plus it tastes more minty. Whereas, you might as well be brushing your teeth with pudding, the way smooth toothpaste feels! Ok, just my personal dislike! :-)