Nut size (A.K.A. diameter) is the size bolt that the nut is used with. The same is true of the thread count. Thus a 1/4"-20 nut fits a 1/4"-20 bolt.
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USS pattern is the most common type of flat washer.
SAE pattern is a tighter fit on the bolt and a smaller outside diameter.
A nut with a built in washer.
Flange bolts have a flange on the bottom of the head that distributes the load like a washer.