Over the years implementations by IBM have been available on many of their operating systems: VM/System?, OS/2, PC-DOS?, MVS/TSO, AS/400?, AIX/6000?. There are other implementations available.
In 1996 ANSI published a standard for REXX: ANSI X3.274-1996 "Information Technology – Programming Language REXX"
Cowlishaw seems to prefer Rexx, whereas IBM sales, ANSI, and the majority of the web uses REXX.