What they are allergic to is something found in the oil of the peanut. That is why they have to be careful about products with the warning "This is manufactured in the same facility where peanuts are used." Many can't even have a peanut shell touch thier skin.

For the other nuts, not everyoen who is alergic to peanuts is allergic to tree nuts. They do have to be careful to not get nuts that are processed and shipped at all with peanuts. Likewise some people with tree nut alergies can handle peanuts and peanut butter. It could just be the case of people with alergies often have more then one and some have both an allergy to peanuts and nuts. They may also not tolerate bees and a few other common allergens

One poor kid in my son's class can't tolerate peanuts, milk products, skin from chicken, and about a hundred other things He deals really well, but it has to stink to always have special soy milks and special treats when the rest of the class is eating the same thing.