Material per ASTM specifications are preceeded by the A, hence the A351. ASME code materials for pressure vessels take this ASTM spec, and then add test requirements to them. The ASME Code material for vessels then gets an S before the ASTM spec, hence the SA351 designation.
As far as I know, this holds true for all the materials. I've looked at a number of them and have never found any differences other than what testing is done to ensure the material complies with the spec.
