I owned and hunted with nothing but Black Widow recurves in the 50 pound to 57 pound range for a bunch of years. I have also owned and hunted with the three Widows that you have asked about.
First the easiest answer. There is no functional or material difference between a PMAII and a PMA III. The only difference between these two bows is the finish. The PMAII is the "Graybark" and it has a gray (more like a greenish-gray) hue to the finish; The MAIII is referred to as the "Autumn Oak" because it has a brown hue to it's finish.
There is a functional difference between a PMA and a PSA. In short, the PSA has a handle that is 2" shorter than the handle of a PMA. The PMA's handle length is 18" and the sight window is 5.5"; The PSA's handle length is 16" and the sight window is 3.5". In affect, the sight window on the PSA is 2" shorter than the sight window on the PMA. Some guys believe a larger sight window facilitates faster target acquisition and improves the overall visibility of the target; other guys won't notice the difference between a 3.5" sight window and a 5.5" sight window unless you point it out to them.
In comparing a 60" PSA to a 60" PMA (Note: both bows have the same overall length in this example) there is a slight functional difference. Because the PSA has a riser that is 2" shorter, this allows for a "working limb" that is 2" longer. Some believe that a longer working limb is smoother to draw and will generate slightly more cast than a shorter working limb. In the hands of an expert archer, this difference might be appreciated. As a practical matter, most archers would not perceive a difference between the performance of a 60" PSA and a 60" PMA.
PSAs are offered in overall lengths of 56"-62"; PMAs are offered in overall lengths of 58"-64". Essentially, the PSA is marketed as a bow for those who like to go "short and light". The PMA is marketed as a bow for those who like a "heftier, longer bow with more stability". As I indicated above, 9 out of 10 guys would shoot a 60" PSA and a 60" PMA equally well and would not be able to perceive a difference in performance between the two bows.
Because of the difference in length in the risers between a PSA (16") and a PMA (18"), the PMA is an ever-so-slightly heavier bow. Black Widow reports that a 58" PSA weighs 3 pounds and a 60" PMA weighs 3.25 pounds. I have owned a 60" PSA and PMA at the same time and could not perceive a difference in weight.
They are both GREAT bows and you will not be disapointed regardless of which model among
these you choose.
Good hunting...