Are ICO and Shadow of The Colossus related to each other?

Question

Now when the ICO+Shadow of Colossus Collection is out for the PS3, I was wondering that are these games some how related to each other? Is it better to play ICO first or vice versa?

EDIT: After getting an answer I searched again and found out that Wikipedia has also a small section how these games are connected to each other.

Wikipedia - Shadow of the Colossus & connections to Ico

Answer 1

Yes, they are. Shadow of the Colossus is a prequel to ICO, set in the same world. In addition, Shadow of the Colossus explains some of the story from ICO. So I would recommend playing Shadow of the Colossus before starting ICO.

Answer 2

SotC and ICO's connection as well as timelines are left up to personal interpretation. The games' creator has gone on record saying he had no idea in mind as to how they both intertwine while creating them other than the fact they both take place in the same world.

Most fans believe SotC is a prequel due to the ending which reveals a baby with a "certain condition".

Have a look at this (slightly spoiler laden) bit from Wikipedia:

Shadow of the Colossus is considered both a spiritual successor and prequel to Ico. For several months during and after the game's release, the game's director and lead designer, Fumito Ueda, maintained that the game's status as a prequel was simply his personal take on the game and not necessarily its canon nature, as he largely intended for players to decide the specifics of the story for themselves, but he confirmed the two do have a connection. Moreover, the shadowy figures which appear in the Shrine of Worship are connected to the shadows which the player must fight in Ico. Both games feature "horned" characters for protagonists (Wander sprouts horns at the end of the game). The Queen's Sword from Ico is also available as a bonus unlockable item. Both games also use unique fictional languages.