I'm confused, IMHO "Schwartzian Transform" and "Decorate-Sort-Undecorate" are two names of the same thing ...

Actually, I had thought that "Decorate-Sort-Undecorate" and GRT were two names for the same thing. A look at the Wikipedia article you linked has undeceived me. (Apparently, even GRT is a misnomer. According to someone posting here at PM, the technique was first published back in the 60s or 70s and only relatively recently made widely known by Guttman and Rosler, for whom it is now named! Oh, well...)