I will support micalbrch's answer and add following:
The difference in requirements between issuing material certificates class 3.1 and 2.2 has for years been about the same, regardless if EN or other worldwide organizations.
Material certificates are issued by material producers and are traceable back to original material and lot. Even if a valve producer normally check all incoming materials, and always buy materials with 3.1 b certificate, it is in itself not sufficient for the valve producer to issue 3.1 b certificates from parts produced from this material.
A valve producer can however issue a function and performance and pressure test certificate grade 3.1 b (or witnessed 3.1 C), but only if he has a working and certified recognized QA system and procedures, enabling him to do this.
With a 3.1 b performance test, material certification will normally follow as a 2.2 certificate of materials (valve producer confirming that materials are correct and of such and such metallurgical quality).
If the end users wishes a 3.1 b material certificate for the valve (say for pressure containing parts) certain procedures must be followed.
Normally this will consist of original material producer issuing a 3.1 b certificate for the relevant parts and with a marking from material producer with traceable marking for each single part through the valve producers production, and a copy of the original parts analysis and test certificates following the parts through production. It might also be necessary with further tests or additional documentation if a component is treated during production, making changes possible in material quality for instance heat treatment.
A typical example is welding, wich will require typically for instance certified welders, welding procedures (doucumented), and sometimes x-ray or other tests confirming end quality.
In all this is not then the valve producers material certification, but copy of traceable original certification with necessary additions.
PS - This is a resume from memory, but all procedures are, as michalbrch
states, clarly described in the relevant EN or other documents, 3.1b and 2.2 not precises descriptions as such but typical 'branch abbreviations'.
If in doubt, a qualified experienced end user will always be able to give details at what the exact requirements are for each project or company or application.
Hope this will help.