The shorter and fatter nut is used for the type of spinner where the mounting plate is in front of the prop hub with a skirt of material towards the rear and the cutouts for the prop in that skirt. Then a nose cone fits onto the rear portion.

The longer nut that is smaller in diameter is not a prop nut at all. Instead it's the extension joiner used for metal spinners that have a screw that runs through from the nose and goes into that long joiner nut. It is intended to be used on the shaft after the other nut has been put in place. But in the picture you have it backwards. The hex on the coupler nut should be against the prop nut hex.

The type of spinner that the fatter prop nut is intended for are very rare now. You could adapt to using the propnut supplied by cutting off most of the part that sticks out past the washer and file the rest down so it's even with the back of the washer. Or you could drill the prop hub part way through to let the stub fit into the hub.

Or you could just go down to a hardware store with your engine and find a couple of cheap nuts and washers that fit the shaft. The price of the nuts and washer from Horizon is .... well... IT'S NUTS ! ! ! !.... Being a Saito I would imagine the thread is metric.