I think, those are differents things
Avisgope please explain, what do you mean with correlation? (relationship?)
There is not any specific relationship with APi, or ASTM.
under ISO, into your processes, yo can use API, ASTM or whatever and if you want to be certified on ISO, go with an ISO CB, and if you want to be certified under API, or ASTM look for those entities which certify you on such standards.
I hope this helps
Pd I´m ISO certified for one side and on the other side , I´m certified on ASTM, We manufacture pressure vessels.