What is hard wheat?

Wheats in the soft wheat class are softer than those of the hard wheat class. The terms ‘soft’ and ‘hard’ as applied to wheats are descriptions of the texture of the wheat kernel.

Hard wheat has a kernel that is high in protein and gluten content. Grain hardness is a character of particular interest the milling and baking industry. Hardness of wheat is a result of the strength of the adhesion between starch and protein in the endosperm.

Durum wheat is a hard wheat, grown mainly in the spring, and is generally milled into a coarser meal (called semolina) rather than flour, though durum flour is an inevitable byproduct of semolina. Semolina is used chiefly for making macaroni, spaghetti vermicelli, and similar pasta products.

Hard wheats result in more damaged starch than soft wheats in the milling process. In bread, this damage largely contributes to the soft texture and the gentle pleasant mouth feel of the crumb; mover starch damage has a retarding effect on the bread going stale.
What is hard wheat?