I can't speak for the PS2 version of Ys III, but Arc System Works actually did the port for Ys IV, I haven't played it in a very long time, but I do not remember them changing too much for the PS2 version (take that with a grain of salt). I'm not entirely sure what documents they were given by Falcom, but Falcom was never exactly happy with Ys IV before the release of Memories of Celceta.
The reason for the two different versions for PCE/TG16 and SFC/SNES was because Falcom passed the project onto two different teams (Hudson for PCE, Tonkin House for SFC). For a while Mask of the Sun (SFC) was considered the canon because it stuck closer the technical documentations given by Falcom. Hudson took some liberties to try and make the setting and plot more marketable (there is a trailer for the pitch for an anime based on this version out there), but in these changes strayed away from the original documentation given by Falcom. With that said it always made me sad that SFC was canon over the PCE game because I had so much more fun with the PCE version.
Ys V for SFC has two versions Ys V and Ys V Expert. Expert was released a few months after the initial release after comments about how easy the first release was. There is also a PS2 remake of this, and was a bit more substantial than the Ys III or Ys IV remakes.
The reason for the two different versions for PCE/TG16 and SFC/SNES was because Falcom passed the project onto two different teams (Hudson for PCE, Tonkin House for SFC). For a while Mask of the Sun (SFC) was considered the canon because it stuck closer the technical documentations given by Falcom. Hudson took some liberties to try and make the setting and plot more marketable (there is a trailer for the pitch for an anime based on this version out there), but in these changes strayed away from the original documentation given by Falcom. With that said it always made me sad that SFC was canon over the PCE game because I had so much more fun with the PCE version.
Ys V for SFC has two versions Ys V and Ys V Expert. Expert was released a few months after the initial release after comments about how easy the first release was. There is also a PS2 remake of this, and was a bit more substantial than the Ys III or Ys IV remakes.