If you've been living under a rock, you probably haven't heard that there have been lots of issues with new oil pumps for your 134 cu in 4cyl. Willys engine. I myself had this issue with the pump locking up and snapping teeth off stuff. Fortunately, mine only broke the oil pump teeth. Some have had the cam teeth break off.
The best way to tell which pump you have is simply look at the cover. The new ones have the pressure release built into the cap. The old style has the pressure release built into the housing.

The internals are totally different too.

One thing I noticed while taking these pictures is the old style pump has an oil galley on the housing so oil can get to the shaft. The new one does not. I wonder if this is the problem with the new ones? You can see the missing teeth on the left side of the gear on the new one.

So here's the scoop, if your original oil pump works fine and your engine had good oil pressure, reuse the original pump. My engine rebuild kit came with the stuff to rebuild the original pump, gaskets and the relief spring.
Mine was properly installed. I had primed it properly and when the engine was running for the first 5 min, it had great pressure, 40 psi, then it shut off because the distributor quit spinning. Mine was a Melling. When I rebuilt the V6 in the Jalopy, I used a Melling pump. I know they make good pumps, but for some reason these just don't work. The drive shaft in my pump is what locked up. The idler gear falls right out into your hand. As you can see in the pictures too, there if very little wear on the cover. So I have no idea why this happened.