> "ANSI" is what people call it when they are working from paltry and incomplete samizdat doco of how this stuff works
People just use "ANSI" as a shorthand for ANSI X3.64-1979. And that was the standard that DEC used for their VT100+ range of terminals, which in turn became the de facto standard from which most modern terminal emulators are derived. If you read the DEC documentation, you'll find many references to "ANSI standard", "ANSI controls", "ANSI colors", etc. I don't think this is because they were ignorant of the subject matter, considering that they were members of the committee that produced that standard.
And ECMA-48 is essentially just the European equivalent of ANSI X3.64, and was developed in parallel. But obviously an American company like DEC or Microsoft would more likely be working from the American version of the standard rather than the European one.