Ahem AKSHULLY

The centripetal force is the one that is directed directly towards the center (hence its name) of the virtual circle your object is rotating about (the blue arrow in this diagram). It is the “physical” force that acts on the object to make it follow a circular path, except it isn’t because that force doesn’t exist either, it’s just a convenient model for billions of billions (of…) of fundamental particles interacting together in probabilistic ways that, statistically, makes the thingamabob go round the imaginary point.

The centrifugal force is, as Black Hat eloquently puts it, the force that appears when you use the rotating object as the frame of reference (which is like saying that the entire world revolves around the object). This isn’t any more or less “correct” than using the ground as the frame of reference (in fact the ground itself is an accelerating frame of reference, which is why the Coriolis effect is a thing, it just is almost never significant except in weather-related applications and using the ground as a frame of reference is usually more useful than a “more stable” frame of reference like the solar system, or the milky way, or whatever, because honestly calculating train arrival times relative to saggitarius A* means that all trains are going about 225000 m/s which is just a pain in the ass to deal with let’s be real).

If you’re trying to build, say, “gravitational rings” for a sci-fi space station, then talking about the “centrifugal force” (which is proportional to the velocity arrow in the previous diagram) is a whole lot more relevant to the people you’re providing fake gravity to than saying “well akshully the force that you feel keeping your feet on the ground of the station doesn’t exist, you just exist in an accelerating frame of reference”.