It was probably called the PSX back when it was the only system because there was no need for a numeric indicator. It wasn't until you got the Playstation 2, that you needed to differentiate between the generations.
Here's how I consider it:
PS1 = Original grey console and games for it
PSOne = The redesigned tiny version with the large power adapter
PSX = Interchangeable with PS1 for the most part, but there was actually hardware from Sony called the
PSX which was actually a PS2 DVR functionality.
The term PSX should have been retired when the PS2 came out, and it
really should have been retired when Sony made other hardware with that name.