menu naigation is more or less identical. i'm sure the ps3 has more options than a psp though. the general idea is the same on both
Nahhh im fairly certain that the PS1 did not use the XMB-style menus. Im almost positive that it began with the PSP and some of Sony's TV's and DVD players.
The "official" Sony PSX is a PS2/DVR combo unit, PSX was just a name used during development of the PS1 that stuck. I don't believe Sony formally referred to it as PSX at any stage beyond that.
Not the OS, the user interface. The PSX was only released in Japan, some people on here have imported them though. Even if you don't use the video recording facilities, they are pretty cool looking PS2's. I wouldn't like to say how much code is shared between them because it's just a menu bar that they have in common. I don't believe the actual OS code is similar. The original question was a bit vague so I'm not suprised the answers have been too.