"Nut" is both a botanical classification and a culinary classification of plant parts.
An indehiscent fruit having a single seed enclosed in a hard shell, such as an acorn or hazelnut.
Botanically, a nut is a type of fruit with a single seed and a hard shell around it that does not split open. Practically, these are going to also be dry on the inside and not have a fleshy bit, like you expect fruit to have.
You would probably consider all botanical nuts to be nuts, but many things you consider to be nuts food-wise are not nuts botanically. Often, these culinary nuts are actually seeds.
- The usually edible seed of [a botanical nut].
- Any of various other usually edible seeds enclosed in a hard covering such as a seed coat or the stone of a drupe, as in a pine nut, peanut, almond, or walnut.
"Culinarily" means in a food context. When you eat nuts, you don't really concern yourself with how your nuts reproduce or whether they used to be in a larger fruit. You kind of just think of smallish dry, crunchy things. Things that are "nutty."
Since that is what society has agreed nuts to be, that really is all you should have to concern yourself with. The botanical definition does not have relevance to you. A nut is a nut.