The American Society for Materials and Testing develops ASTM material standards, which can include the chemical, mechanical, physical, and electrical properties of a material. Standardization includes both a description of test methods to be used on building materials, as well as dimensions and shapes for these materials. ASTM standards can be required of building materials like concrete before they can be used in construction.
The American Society of Mechanical Engineers sets the ASME standard. ASME material specifications are based on those published by ASTM, AWS, and other recognized national and international standards. In the construction of infrastructures such as bridges, power plant piping, and boilers, ASME standards are legally required. ASME b16.5 is commonly used.
You should be aware that while most ASTM and ASME specifications are nearly identical, there are many ASTM materials that cannot be used for ASME code construction. As long as the material is produced in compliance with both specifications, it may reflect a dual ASTM and ASME specification on the material and on the certification process