A high hex nut is designed to go onto a bolt with matching threads. They are called high because they are bigger in in most dimensions than a standard finished nut. They aren't as tall as a coupling nut, though.

While often double chamfered and countersunk, they are can be only single chamfered and countersunk, especially in larger sizes. They are only available in steel, and usually only grade 5 and 8.

If you don't need the grade 5 or 8 versions, you may find a hex coupling nut will suit your needs better as they come in a wide variety of materials, lengths, and outside diameters. A high nut has set dimensions.