Peanuts are neither the nuts of peas, nor peas, and, in fact, they are not even nuts.
According to Live Science, the nut category of food has a lot of non-nuts in it. Almonds, pistachios, peanuts, pecans, and cashew are not nuts.
By definition a nut is a dry fruit with a single seed encased in a hard shell, which doesn't open on its own. Walnuts, which are true nuts, are a good example.
Peanuts don't fit into the nut category because they have two seeds and easily break open. They grow in a pod and that makes them a legume, plants that produce fruit in a pod, like snow peas.
Meanwhile, almonds, cashews, and pecans are actually drupes, seeds that grow inside a fleshy outer layer surrounding a pit that contains a seed. A peach is a drupe and we eat the juicy outside layer and discard the seed. With almonds, cashews and pecans we remove the outside layer and eat the seed.