From Bulbapedia, the community-driven Pokémon encyclopedia.
Each location in Pokémon Colosseum and Pokémon XD: Gale of Darkness has its own identification number used internally by the game, mostly to display where a Pokémon was caught. In contrast to the handheld games, a Pokémon's met location in these games is stored in a two-byte number. These values are enumerated below.
When a Pokémon originating from Orre is traded to a handheld game, those games will display "met in a trade" in the Pokémon's met info. If they are transferred to Generation IV, the met info in those games will describe it as being from a "distant land", the same as for Pokémon from the handheld Generation III games.
If a Pokémon from Pokémon Colosseum or Pokémon XD gets traded to the other game and the Pokémon's Original Trainer data matches the player's data (a rare occurrence), the game will interpret the Pokémon's met location number using its own data, meaning the met location it displays will not match the Pokémon's true met location. This is because, even though both games feature some of the same locations, no met location indices match to the same string between games.
There are a couple of special cases as well in Pokémon Colosseum and Pokémon XD that disregard the met location number entirely. In Pokémon Colosseum, if a Pokémon is Espeon or Umbreon and its Original Trainer and origin data matches the player and Orre, then their met info will say "<Player>'s old friend." In Pokémon XD, if a Pokémon is Eevee or one of its evolutions and its Original Trainer and origin data matches the player and Orre, then their met info will say "Obtained from <player>'s dad."
Any numbers not listed below will either display "met at a distant land" or "met in a distant land", depending on the game.