m2 is true elongation at true ultimate stress.
To convert the material Engineering Elongation specified in the material spec (i.e. E = 35%) to True Elongation, use ln(1+E/100). This is what Table 5.7 does, and if you do this, you get a similar number to m2.
The number before this equation is a material constant. 3x for Stainless, 2x for Ferritic, 1.3x for Aluminium are all material constants dependent on factors such as grain size, cleanliness, inclusion content etc. that contribute to voiding and microcrack initiation.
αsl is another material constant dependent on metallurgical (crystallographic) structure.
Stainless steel is better for intense cold working and cold stretching, therefore I would expect it to be better for local failure, hence the higher material factors.
It looks like if you set the Uniaxial Strain Limit to m2 as per Note 1, then you get a conservative result. I don't see why you would do this. You would always have a material test certificate with details on elongation, or ASME Part 2 provides minimum acceptable elongation for each material.
ASME PTB-1 provides comprehensive detail on the local failure method, including derivation of the big local failure equation.