You can horse around trying to codge together all kinds of A4-compatible parts if you want, or you can just go to Moyer and get the perfect part the first time. And the advice you need to make it work. And probably a hundred posts from other people talking about how they did it on their specific boats.
I buy spark plugs locally, but everything else I get from Moyer. Maybe this costs me $25 a year that I could possibly save if I spent a lot of time looking around, but it isn't worth the risk of getting the wrong part and my time is worth a lot more than $25 (to me, at least). I'll buy cheap tools for projects I think I'll do only once, and I'll buy cheap ice, but trying to minimize engine part costs is a waste of time and peace of mind. His specialized water pump is the best there is for the A4, ESPECIALLY if yours is hard to access. Also, his "Extendo" bolt for the water pump. And the carb intake thumbscrew, the carb mix thumbscrew, the electronic ignition, the CORRECT coil...the only enhancement of his I haven't put onto my engine is the antifreeze cooling, and fortunately I haven't needed many rebuild parts.
All those terms you mentioned that sound confusing are not really complicated but are meticulously documented on his website. And if you don't understand what they mean, rest assured the person you're buying from will either need to know or will not know, and you are going to end up with the wrong part. Half-a$$ed parts like bad head gaskets and water pump seals translate into screwed-up engine, and were the reason A4s developed a bad reputation after Universal stopped making them - well, that reason has gone away entirely due to Don Moyer's efforts.
Old style - older engine shape with a distinctive "tombstone" cover; a small number of parts fit the old but not the new and vice versa (I believe all consumable parts like pumps and gaskets fit both old and new)
160 degree - temp you can run at with antifreeze cooling (this determines which thermostat you use)
140 degree - temp you can run at with raw water cooling
Oberdorfer - type of raw water pump, says OBERDORFER on the impeller cover, I believe this term exists to distinguish the stock A4 pump from the Moyer version, which has sealed bearings and thumbscrews on the impeller cover - it is a significant improvement over stock. I've rebuilt the Oberdorfer pumps several times and never ended up with a great outcome. The Moyer pump will probably never have to be rebuilt.
By the way, I don't run my raw-water-cooled engine with a thermostat, and haven't done so for 21 years. I've blocked off the bypass at the tee coming out of the side of the head, forcing all the water from the pump through the head for maximum cooling effect. Yes, the engine runs cold, and I head off sticking valve potential by adding a few ounces of Marvel Mystery Oil to the fuel, but the engine will not overheat...and overheating is death to these engines.