For the most part, even though there are competing testing labs, there is only a single set of standards created by UL and used by the other firms.
CSA and FM make their own. There are also several IEEE, NEMA, IEC, and ISO which are all independent. And ANSI and ASTM and ICEA. The odd one is Pennsylvania has a couple specific standards unique to them.
UL.com only tests to UL.org standards. FM is similar. The others will test to almost any standard. Where this matters is if for instance you use an ETL part in a piece of equipment UL will NOT List it but anyone else will.
The only one to watch out for is CE. Companies are allowed to self certify under that one if they use “similar” materials!
The other odd one is that MSHA has a testing lab for mining equipment but it is NOT recognized as an NRTL by OSHA.
By way of examples there are some portable cables that are NEMA standards that are Listed by CSA. For instance DLO is NEVER UL stamped. DLO is a NEMA standard although NEMA is a pass through for the underlying ICEA standards in this case. It is therefor allowed by NEC but not a UL standard nor a UL Listing.
UL heavily promotes the myth that they are the only game in town and charge a huge premium for it. While I agree they are pretty good the idea that they are the one and only standard is simply not true.