From what I understand,
The 590 A1 or Milspec is the version that was tested by the military and meets military standards. The major differences btw a 590A1 or 590 special purpose is that the A1 has the following:
1) Heavier barrel
2) Metal safety
3) Metal trigger guard
To most people, the differences btw the 590 and 590A1 are miniscule and not noticable.