"A laughable claim, Mister Bond, perpetuated by overzealous teachers of science. Simply construct Newton's laws into a rotating system and you will see a centrifugal force term appear as plain as day."
https://xkcd.com/123/
I know I've had it explained a million times to me since I was a kid but... I still can't remember the difference between the two. I do, however, remember this little factoid about it.
I think centripetal force is whatever is pushing/pulling the object toward the center of rotation, such as the closed door of a car pushing on you while driving around a curve, where otherwise you would fly out of the car. Another example is the wheels of the car causing it to travel on a curve instead of straight. Or the rope of a tetherball for a pulling example.
In most cases (besides orbits in space) the force is question is actually the electromagnetic force, like any other case where objects made of atoms touch.
Personally I think it's weird to call that a specific force, especially by those who don't want to give centrifugal force a name - sure it's really just things "tending" to travel straight instead of following the curve, but no reason that can't have a special name, it's certainly intuitive enough.