ETL stood for Electrical Testing Labs, a competitor to UL. They had a hard time making it and almost went under, but were bought by Intertek. So intertek is the company, but they retained the ETL logo because it was well known. Not as well known as UL, but more well known than anyone else.
ETL, and now Intertek, never created their own testing standards, they used ULs standards. But they did their own testing and applied their own marks, usually for less money than UL charged. Some people said they were easier to deal with than UL, others said they were easier because they were less stringent. I personally experienced that when they were ETL but that likely changed when Intertek took over because that reputation was one of the things that was hurting ETL. Whether or not the word Intertek appears on the logo is likely just an issue of the age of what you are looking at. Could also be a counterfeit though, that’s been happening a lot on all fronts, UL included.
As it stands now, both UL and Intertek/ETL are what are called an “NRTL”, Nationally Recognized Testing Lab. When a code calls for using a “listed” product, they are meaning listed by an NRTL. A list of accepted NRTLs is kept by OSHA and you can look at it
here. You will see that UL is on there, as are CSA and Intertek/ETL, as well as several other lesser known firms. All of them are acceptable in most jurisdictions.