To my understanding,
1 - Lubrication quality and sticking quality to metal based on viscosity
2 - Pumping especially at cold start
3 - It's behaviour at different temperatures (multi-grade function like xxW-yy is multi with xx and yy grades)
4 - It's resistance to burning, handling Carbon produced by combustion.
5 - Sludge and waxes left behind by oil
6 - Allow temperature to pass on to cooling system, no heat residual within.
First thing to know is, why there are different Qualities (from different manufacturers) for same Grade, because the same grade can be achieved by different type of minerals, different type of additives company research on and if purely synthetic then again the base chemicals company researches and works on.
With different minerals/bases, behaviour of oxidation/burning with fuel is different and quality of mineral tells if it will burn, how much. AND based on general behavious of diesel, petrol and CNG, oils are made to handle after burns, resistance etc.
Fuel burning,
Diesel system doesn't use Spark plug and purely burns on heated and compressed fuel and air, it's combustion creates more Carbon and heat and power too as being used in trucks etc.
Petrol burn quickly and every fuel provider uses it's own technology of refine and additives here PSO, Shell, Caltex , Total. Everyone gives it fuel some letters.
Gas is mainly compressed natural by SNGPL etc. but Compressor systems produce different qualities at pumps.
I was studying one place they are using technique to use Diesel engine burn CNG (65%+35%) and basic ignition is on compression as of diesel. Here our VAN masters changed their Engines to Petrol (costly) and now weep on two days OFF.