Growing up as Indonesian I don’t know there is a difference between nut and bean. Both of them are ‘kacang’ in Indonesian. And I hate them both. And nope, I don’t have any nut allergy.
Coming to Australia I encountered people who doesn’t eat nut but eat bean, and vice versa. It still strange for me because both nut and bean are just the same thing—‘kacang’—for me.
So, what is the difference?
Most nuts are fruit, the dry fruits. They grow on trees, hence they are called tree nuts. Example of tree nuts are chestnuts, hazelnuts, almonds, and walnuts. "They are usually enclosed in a leathery or solid outer layer. In botany terms, nuts are strictly a particular kind of dry fruit that has a single seed, a hard shell, and a protective husk," according to the U.S. Forest Service.
Some nuts are not fruit—they are legumes, such as peanuts. Peanuts grow underground, as opposed to nuts. However, usually for culinary and research purposes peanuts are classified as nuts.
On the other hand, beans are seeds. You can plant beans and they will grow becoming plants, such as green beans become bean sprouts.
Looking up on the shell, nut and bean have a distinct difference. Nut shell is hard and usually only contain one seed. Contrarily, bean shell is usually soft. Some beans, like peas contain many seeds inside. There is also a lighter part on the bean shell, called a hilum, this is the part where bean plant grows.