PSX was actually the codename and the abbreviation is PS. PS One was the smaller redesigned version Sony released in 2000. The PS One is very charming with its small form factor, probably my favorite console of all time. I own both to this day.

They want you to buy their new games. They also want you to be more likely to buy the old games again when they eventually do a sloppy re-release of the old games or tie it to increase the value of their subscription offerings. Basically to make more money.