How many versions of "Ico" are there?

As seen on this question about Ico, there are different versions of this game with slightly different puzzles in some rooms. Many walkthroughs and youtube videos published show different solutions for the version I played in PS2 & PS3. What version was the first and how many are there? It is related to the region, may be? Thanks in advance.

With respect to gameplay, there were two versions released for the PS2 (an original version and a U.S. version), and one remake for the PS3:

          U.S. Version               Original Version

          PS3 Remake

With respect to language and region code, there were eight releases, including one reprint in Europe coinciding with the release of Shadow of the Colossus:

PlayStation 2

NA September 24, 2001
JP December 6, 2001
EU March 22, 2002

Re-Release

EU February 17, 2006

PlayStation 3

JP September 22, 2011
NA September 27, 2011
AUS September 29, 2011
EU September 28, 2011