PS3 is when you have an actual physical PS1 disc thrown into the PS3.

PSVita/PSP/PSTV are to differentiate the Japanese PSN release, so you know which console it's on exactly (don't ask why it isn't merged with PSN lol)

PSN is just the actual Japanese PSN release played on PS3.

Here's a very long link, actually.

PSTV I have no idea if it actually exists but eh big shrugs