Technically a peanut isn't actually a nut at all: its a legume or "bean."
And that is the big distinction. Since they are technically different things, the allergies that people have to them are going to be different. Since production of some nuts can happen in the same plants that peanut products are produced in (they are commonly in the same products or you have companies that make products separately but produce them in the same plant for cost reasons).
Peanut allergies are a serious thing and that's why you label them on products that contain non-peanuts - they are typically made in the same plants. Just calling them nuts just isn't enough.