I have been told that Wishes work differently in Commander than in normal casual Free-For-All (FFA) mtg. Do the comprehensive rules cover how wishes work in Commander? Do the rules for wishes differ from normal FFA multiplayer?
Wishes are non-functional in Commander, unless your group specifically allows them and defines where they work.
Abilities which refer to other cards owned outside the game (Wishes, Spawnsire, Research, Ring of Ma'ruf) do not function in Commander without prior agreement on their scope from the playgroup.
Basically the Rules Committee's reasoning was that using wishes in their original, casual-play way (searching your entire collection) wastes too much time in play1. So they used to restrict you to searching your sideboard, which is how wishes work in competitive MTG. However, Commander's sideboards are "optional" and Sheldon has generally come out against them, so the default is that wish cards don't work at all.
Sideboards still have to follow all the normal deck-construction limitations, like in any other format; for Commander, this means you can't have break the one-of restriction or violate color identity just because a card is in the sideboard. Thus, if you group agrees to play with wishboards, you'll still be limited to your commander's color identity.
(Note also that the official sideboard size is 10 cards, not 15 like 60-card constructed.)
1 – Which is also why Shahrazad was finally banned after some time as the only Vintage-banned card legal in Commander.
I have done a search for all Commander references in the CompRules and have found nothing specific. There are several points to consider when determining this question in particular:
Commander is a semi-official format. It's covered in the official rules, but it has been invented and is maintained by regular players. So questions specific to the format that are not answered by the CompRules should be probably be asked and answered there.
Going by the rules, I would argue that Wishes work the same as in regular games: Since a Commander game is casual only, you are allowed to get any non-ante card from your collection. In sanctioned events, Wishes can only get cards from your sideboard.
Going by the philosophy of the format, Wished cards should probably be restricted to cards in the Commander's color identity. But that is more a house rule, as the CompRules don't regulate that particular point.