The yellow chocoo is the chocobo you start out with. It can run over land.
When your yellow chocobo is upgraded it becomes light blue. With this chocobo you can go over shallow water.
After that, your chocobo can upgrade to red. This chocobo can go over mountains.
You then can upgrade your chocobo to dark blue. This one can go over deep water.
Finally, there is the gold chocobo, the strongest of them all. It can fly and do all the abilities the other chocobos can.
Now when you receive a chobobo,with it you get to play the Chocobo Hot and Cold Game. This fun little mini game can get you some very rare items, even Zidane's Ultima Weapon. This side quest is very time consuming. It also allows you to fight the hardest Boss in the game, Ozma.
To get started, go to the Chocobo Forest on the Mist Continent. It looks like a perfectly circular forest. Enter the forest and Mene, a moogle, will show you Choco. You now can play the Chocobo Hot and Cold Game. Talk to Mene and you will be able to pay 60 gil for 60 seconds. Press the square button to search for items. You really need to memorize the different squawks that Choco makes. Once you find a treasure tap the square button quickly. When the depth gauge reaches 0 you get to keep whatever you dig up.
Chocographs
After playing Chocobo H. and C. for a bit you may dig up a stone called a Chocograph*. Mene will examine it and tell you, you can find treasure on the world map. Now leave Chcocbo forest. Press triangle on Choco and choose to open the Chocograph menu. Highlight your chocograph piece and exit the screen. Now a picture will be above the world map picture (world map must be open.) Find this area in the world. Choco says the same things when you are on the world map as in the Chocobo H. and C. Game. Hit square to dig. when you are in the exact location of the picture and hit square you will uncover a treasure. Either you will recive a lot of treasure or you will recieve a Chocobo skill and change to a differnt color. When your chocobo recives a skill you will have a new ability.
*Chocographs and Chocograph Pieces are two differnt things. Chocograph pieces tell you how to find Chocobo Air Garden.
That is all the information I have on Chocobos.