I guess I'm just saying I don't understand the process, of why they exist, and what their intended use is.
It's a history lesson if nothing else.
IEEE (Institute of Electrical and Electronic Engineers) is a "society" of electrical engineers. They adopted a set of "best practice" standards a long time ago that they continually maintain, which have been adopted and referred to by many other organizations. But they are NOT legal documents in any way shape or form. However, if you are a PE and IEEE member and you design or approve something that is in clear conflict with IEEE standards, you can be held up for ridicule by your fellow engineers, even kicked out of IEEE. Getting kicked out is tantamount to being ostracized in the engineering "country club". But it's not as severe as, for instance, being a lawyer and getting disbarred by the ABA because you need the ABA certification to practice law, you do not need IEEE membership to be a PE. You might end up finding it difficult to get work however.
ANSI (American National Standards Institute) is similar to IEEE, but in actuality is broader in scope, covering mechanical, civil, chemical etc. engineering disciplines as well (think ANSI bolt grades and oil viscosity specs). They used to be separate, but for the most part the electrical standards of ANSI are now administered by IEEE. Essentially, IEEE are the working authors and editors, ANSI is the publisher.
NEMA (National Electrical Manufacturers Association) is a set of standards created and adopted voluntarily by a group of the largest electrical equipment manufacturers so that there were clear standards by which components and systems could be referred to and compared against. They too are NOT legal in any way; strictly voluntary and, more importantly, self regulated. So one could make an argument that it is a set of rules by which the foxes have agreed to guard the hen house. But in reality, the NEMA standards were a way of establishing MINIMUM performance standards so that one bad apple would not cause a loss of consumer confidence in the entire industry. Still, there is no "enforcement" of NEMA standards other than if a manufacturer uses a reference to them and is proven (usually by a competitor) to not be in compliance, they can be sued to stop using the term "NEMA". They cannot however be forced to change or cease marketing their product.
UL is where you start approaching quasi-governmental authority. UL stands for Underwriter's laboratories. If you recognize the word "underwriter" in there and it makes you think of an insurance company, you would be barking up the right tree. UL is all about testing for safety, mainly fire safety, so that insurers can be satisfied that products so tested and listed have not been marginally designed and potentially causative of losses. It must be pointed out however that UL traditionally is not a QUALITY or FUNCTIONALITY testing lab per se. There is an old saying that you can UL list a bathtub as a busbar if it doesn't start a fire. Not exactly true, but it makes a point. What has changed in recent years is that the NEC now REQUIRES listing by an NRTL (Nationally Recognized Testing Lab) if such a listing can be shown to exist. UL just happens to be the biggest and most recognizable NRTL, but they are certainly not the only one any longer. In fact, many of the smaller NRTLs such as ETL use UL's testing procedures anyway, they just charge less to do it.
Bottom line though,
the AHJ is the ultimate authority in YOUR installation. If he wants to insist on your meeting an IEEE spec or an ANSI spec or an NRTL label he can do so. You can always challenge him, but you will find it difficult to get another authority, namely a PE, to want to contradict an IEEE or ANSI specification if that is what the AHJ is insisting on. NEMA, maybe, because NEMA is not really recognized as a valid test procedure by the NEC; however be aware that for electrical equipment in the US, UL had all but adopted the NEMA standards anyway. So if the AHJ slips up and says he insists on you meeting a NEMA spec and you challenge it, he may be able to just say "Oops, I meant UL" and you are sunk because UL is an NRTL and IS supported by NEC regulations.
Only the lawyers will make out in that situation.