Peanuts - pea or nut?

Apparently, before I came on the scene, my new family used to grow peanuts.  Now I always thought that peanuts were a nut.  But I've been informed that they are actually a pea or part of the legume family if you will.  There are many different types and they can grow on a bush or a creeper.  But unlike peas, peanuts don't actually grow on the bush, they grow under it.  They grow in the soil, but not as a root like potatoes or carrots.  The flower which is on the plant, is pollinated and then a stalk which comes from the flower imbeds itself in the soil and a peanut pod grows with between one and four peanuts.