Group # 8.203, Part # 594181 & 594182 are the '37-'38 1/2 and 3/4-ton panel truck fenders. These are narrower than the PU fenders as they bolt into the wheelwell of the body like a car fender. Part of the wheel/tire is enclosed by the panel truck body. The fender bolts are installed "vertically" if you can picture that. These are specified for commercial "single unit" bodies. Single unit means panel, canopy express, and Suburban. Commercial means the lighter trucks, the larger 1-1/2 tons trucks are called utility trucks.
Group # 8.203, Part # 594855 & 594856 are '37-'38 1/2 and 3/4-ton PU rear fenders. These are wider than the panel truck fenders, as they have a flange to bolt "horizontally" to the box side. The wheel/tire is totally enclosed by the fender. These are specified for commercial cab and chassis bodies. That means a PU style truck with a cab and seperate box.
Both fenders will look the same on the outer 1/2 of the fender, the difference is in the inside 1/2 of the fender where they bolt to the body or box side.
The larger fender you have will look like the correct fender, except on steroids. It will be larger overall, and have a larger wheel opening for the 20" wheel and tires used on the larger trucks. This fender is worth much less than the same fender as a 1/2-ton would use. Many times the larger fenders are incorrectly advertised on ebay as fitting the smaller trucks, when in fact they don't as you found out. About the only way to learn the difference is to do what you did, and buy one and figure it out. I'm a slow learner, I made the same mistake more than once!