gfretwell, those are good questions.
"NRTL" is short for 'nationally recognised testing lab." Oddly enough, this is a term 'invented' by UL at a time when they felt that, in most cases, they had no other competition. UL reps encouraged government bodies (of every size) and specification writers to put this term in their rules.
Then things began to change.
The vast expansion of the Federal Government in the '70's in turn led to various laws 'encouraging' Federal agencies to adopt already existing 'generally recognised industry standards.' One result of these laws was an explosion in sundry industry and trade associations - all of whom saw an opportunity to get 'on the inside track.'
Every trade group has a somewhat different focus. This, as well as UL striving for "ISO 9000" certification, in turn opened the door to an assortment of testing and certification bodies.
UL claims to 'test for the public safety.' UL has absolutely no interest in the performance, quality, or design of a product submitted. If UL 'listed' automobiles, the same standards would apply to bith Ferrari and Yugo ... but no one would ever imagine that the two were "equivalent."
Until VERY recently, UL pretended that NEMA did not exist. UL had it's own classifications (for instance) for enclosures; saying "Nema 4" meant nothing to UL. UL did, however, use this as an example of 'what made UL special.'
Unlike the common practice of letting the manufacture certify such things, UL stressed that UL was independent, did their own tests, AND followed this up with regular factory inspectiona and re-examination of products. UL asserted that this was more reliable than simply trusting to the manufacturer (and the market) alone.
Sometimes -as in the case of fire sprinkler heads- the UL mark says a lot about the product. UL has been heavily involved in the testing of those for a very long time, and many of the tests are 'performance' tests. In other cases -you home computer being one- the UL mark means very little beyond 'it ought not shock you.'
That same home computer, however, is likely to have a legion of other certifications, many of which relate to the performance of it.
These days, "NRTL" can mean most anything the AHJ wants it to mean. UL no longer has the near-monopoly that they once had. If another lab (and there are some) got ISO recognition for testing to a particular standard, there would be little reason for an AHJ to refuse to recognise the new guys' label.
To that end, many government agencies compile lists of the specific certifications that they are looking for.