Bill,
My understanding of the differences between an engine oil primarily for an otto cycle gasoline engine and that for a diesel is that:
1) gasoline burners get lots more moisture into their oil, and also often get sulfur or chlorides (as salt dissolved in water) in the gasoline. The result is acidic products of combustion along with water in the crankcase - bad news. Accordingly, gasoline engine oils tend to have elaborate buffer systems designed to neutralize the acids as they arrive in the crankcase, along with anti-foaming and anti-emulsion additives designed to do as much as possible to make sure that the water goes away quickly when the oil gets hot enough.
The other worry back in the day was dilution with fuel, but the advent of closed-loop fuel management systems and port fuel injection has mostly made that one disappear.
2) diesel engines run lean 99% of the time and the fuel is injected near the middle of the chamber - a long way from the piston rings. So the whole combustion event also happens a long way from the rings. The result is that there is much less moisture getting into the crankcase. There's also less attack of the oil film on the cylinder walls, which contributes to the long-life reputation of most diesel engines. The fuels may (previously) have had a lot of sulfur in them, but diesels tend not to let many combustion products into the crankcase. Also, diesels tend to run hotter down below than gasoline engines, which, again, improves moisture boil-off. The result is that oil has a pretty nice time in most diesel engine crankcases. The additive packages do have some buffers to deal with sulfuric acid (much less deadly to metals than halogen acids like HCl are), but most of the additives are extreme pressure additives (like ZDDP) and lots of detergents to keep the soot in suspension so that the filter system can get to it.
Accordingly, you have a class of premium diesel oils out there sold for "million-mile" use. Basically, you just test them for additive package breakdown periodically, and change them when the oil finally gets worn out at some very high mileage. The engine will burn enough oil to require top-ups which replenish the additive stock significantly.
There have been moves to do this sort of thing with gasoline engines, but generally the upper end of life for oils in gasoline engines is in the 500 hour range with a really large variation depending on engine design and drive cycle. You end up spending a fair amount in lab charges to do the testing frequently enough to catch the oil degradation before something starts eating your chevy from the inside. On something like a Cat or Cummins in a road tractor, you have gallons of oil in there and expensive filters, so changing is a much more expensive proposition and testing charges become a relatively smaller cost.
Generally, though, most oils for light-duty diesel use look a lot like oils for general automotive use. Sure enough, a lot of oils are rated both for S and C class service, though usually to different severities of rating.