Question about welding certification

Can someone knowledgeable on this topic please help explain the following:

Is there a general “welding certification” that you can get? Or does your certification have to be tied to a specific welding process and/or material type? Can you get a certification as an individual or does a certification usually occur through an employer for a specific type of welding that they need you to perform? I assume the general governing body for certifications is AWS and ASME?