Is a walnut a nut or a drupe?
Short answer
Walnuts are classified both as nuts and drupes ('stone fruits').

background
According to University of Wisconsin - Madison, Department of Botany , hickory and walnut can be classified both as drupes and nuts, but are best classified as nuts.  

Nuts fall into the class of indehiscent fruits: dry fruits that do not open when mature to shed their seeds. Many of this group are one-seeded fruits, such as the nuts. In addition, nuts have a thickened and hardened wall. Examples are beech, chestnut, oak, hazel, walnut and hickory. Because of extrafloral bracts, or "husk", the latter two fruits are sometimes called "drupes").

As opposed to indehiscent fruits, the fleshy fruits have a wall that becomes soft and fleshy as it matures. Drupes ('stone fruits') fall into this class. Drupes one-seeded, simple fruits developed from a superior ovary in which the innermost portion of the wall (endocarp) becomes hard and stony, the outermost part (exocarp) becomes a relatively thin skin, and the middle portion between the skin and the stone (mesocarp) becomes either fleshy or fibrous. Examples are cherry, coconut (the endocarp is the thick wood shell that surrounds the fleshy and liquid-filled seed), but also walnut and hickory. The latter two are, however, best called "nuts".

Indeed, according to a popular scientific article in the Guardian, many tree nuts are also drupes, including walnuts and pecans.