There are atleast 2 distinct versions of Final Fantasy X (FF-X): the international version which has Dark Aeons and a revised sphere grid, and the US release. I'm not sure if the US release is same as the original Japanese one.
How many different versions exist, and what are the gameplay differences between them?
There are only two released versions of Final Fantasy X: the regular edition and the international edition.
The regular edition was released in the Japanese and North American regions.
The international edition was released in the Japanese and European/PAL regions (released simply as Final Fantasy X there). It contains the things you listed:
as well as a number other minor changes, as detailed on the Final Fantasy Wikia:
The Dark Aeons and Penance, all powerful superbosses, were added, as well as many minor changes to dialogue, scenes, the Celestial Weapons' key items (Japan only), characters and armor & weapon customizations, such as Ribbon. The release also includes a bonus disc with behind the scenes making-of features of Final Fantasy X, and a special movie prologue to Final Fantasy X-2.
The European release has the the Dark Aeons and Penance, as well as the new equipment abilities, but didn't change the name of the Celestial Sigils and Crests. As with previous PAL conversions of Final Fantasy installments, the game has noticeable black borders and a slower running-speed as a result of poor PAL conversion. The black label version includes a bonus DVD with the title Beyond Final Fantasy, which includes various interviews with the game developers, as well as two of the English voice actors. Additionally, it also includes trailers of various Square games, an art gallery, short biographies on Nobuo Uematsu and RIKKI, as well as a music video of RIKKI performing the song "Suteki Da Ne".
Some versions of Final Fantasy X: International have a glitch, whereby if the player goes to the area where they fight Dark Ifrit it is possible to slip past the men blocking the way to Home, and thus, be able to return to the story at the events in Home with Yuna in the party. This glitch can be repeated after the first time it is used.
