Since Group IV is PAO, there really is no such thing as "Group IV dino oil." Group III is blended into some manufacturer's conventional oil to aid in oxidation stability, but if the majority of the base oil is Group III it's usually labeled as a synthetic.
Group II and III are usually produced by the same means, namely, hydrocracking and/or hydroisomerization. Group II and III both have aromatics at less than or equal to 0.03% and saturates at greater than 90%. The difference between the two groups is viscosity index: Group II is 80-119 and Group III is greater than or equal to 120. The quaility of the refining comes into play when judging Group II and Group III base oils because (obviously) a base oil with 99.9% saturates would be desired over one that just barely met the spec of 90%.