I would agree with TVP, your original post is too broad to answer. Two additional comments - allowable stresses are those stresses that a designer selects as the maximum limit to either avoid fracture (exceeding the ultimate tensile strength) or permanent deformation (exceeding the tensile yield strength) in service.
Regarding the modified version, I have seen this stated from various suppliers and the difference between 8630 and 8630 mod are slight variations in chemical composition in terms of Mn (slightly higher min/max than the standard min/max range for 8630), lower P and S contents, slightly higher min/max range for Cr, Ni and Mo. Overall, the modification to the standard alloy seems to increase hardenability.