Scope and audience. ASTM covers the alloy for general industry: composition, mechanical properties, dimensions and tolerances. AMS is the SAE aerospace material specification and usually adds process control, cleanliness, grain size and inspection requirements on top. Aerospace drawings cite AMS; industrial ones usually cite ASTM.
One standard per product form
ASTM nickel and stainless standards are organised by form rather than by alloy: B637 for bar and forging stock, B670 for plate, B163 and B407 for seamless tube, B564 for forgings. A single grade therefore appears in several ASTM standards, and the order has to name the right one.
AMS works the other way, with one number per alloy and product form combination: AMS 5662 for 718 bar, AMS 5663 for 718 forgings, AMS 5391 for cast 713C. Aerospace buyers quote the AMS number and expect every requirement in it to be met.
What AMS adds
Process control that ASTM leaves to the mill: melting practice, cleanliness ratings, grain size limits, the frequency of mechanical testing, and how the material is identified and packed. Some AMS numbers also fix the heat treatment window more tightly than the ASTM equivalent.
The practical effect is that AMS material is a narrower product. It usually costs more, and it can take longer, because not every heat will meet the cleanliness and grain size limits.
Choosing between them
If the drawing goes into an aircraft engine or a flight-critical assembly, the AMS number is the requirement and there is no substitution to discuss.
For industrial service — chemical plant, power generation, oil and gas — ASTM is normally sufficient, and paying for AMS control on a part that will never fly is money spent on paperwork. If a customer's end user insists on AMS, that has to be visible at the enquiry stage.