Most jars on the shelf contain far more than peanuts. Added palm oil, sugar and stabilisers keep the texture smooth and the price low, but they also change what you are actually eating.
A good jar has a short ingredient list: peanuts, and perhaps a pinch of salt. Here is what each additive is doing, why natural peanut butter separates in the jar, and how to store it so it stays fresh to the last spoon.