Machine Screw nuts and Finished Nuts are the most common nuts used. Finished nuts start at 1/4" sizes and are generally a slightly thicker than machine screw nuts. Machine screw nuts makeup the smaller size range (#0 to 3/8", but most commonly stop at #10 or 1/4"). Both are virtually identical six sided internally threaded nuts, with the machine screw nuts being a bit thinner than their Finished nuts cousin.
Nuts are sized according to their mating screw, bolt or rod that they will be used with, so a #10-32 screw, takes a #10-32 nut and #10 washer.