IRC's (Industry Recognized Credentials) could be related to regional industry requirements but in most cases, I think the reference is to "Nationally Recognized" credentials. Deciding WHO the "recognizing authority" is can be tricky. 

American Welding Society

Some of the common welder testing programs that are often considered to be "Industry Recognized"  are the AWS SENSE program and also the AWS Certified Welder Program. These could be entered into in much more detail but that could be another lesson by itself. The SENSE program is more than just a welding test. 

If you would like to see a page written (unofficial) that talks about both programs, go to http://weldingclassroom.com/learning/aws-sense-or-aws-certified-welder

NCCER

Well, as far as I know, there is no NCCER program for "certification" of welder performance qualification tests. It is my understanding that SENSE has taken care of that.  If you take a look at the link at https://www.nccer.org/workforce-development-programs/disciplines/craft-details/welding and scroll down for the Assesments. You will notice NCCER does not have any. 

NC3

This is a "New Kid in Town" and is separate and apart from any others. It is spoken of as "Industry Recognized" and I imagine like any of the others, it depends who you speak with in industry. Knowledge and SKILL. It is not just a welding test.  Take a look at their brocure at https://www.nc3.net/wp-content/uploads/2019/08/LEEPS-ULINC-NC3-Brochure.pdf