So you want to get in on the Chocobo Breeding business eh? Well to start off, there are 5 different types of Chocobo's. Each of them each have a specific type of terain they can travel over, except for the Gold chocobo which can travel over any type of terain.

Types of Chocobos

Color
Description
Yellow This is your basic Chocobo. They can only travel over flat land. They can't travel over water, moutains, or any other land type.
Green Green Chocobos are the same as yellow ones, except that they can travel in shallow waters, just like the Tiny Bronco does.
Blue Blue Chocobos love the water. They can travel over the rivers as well as the oceans. They can also travel over regular flat land.
Black The Black Chocobo can travel over flat land, shallow waters, and mountains
Gold This is the ultimate Chocobo. Not many of them exist in the world. The Gold Chocobo can travel over all land types. You need this Chocobo to obtain the summon Knights of the Round, which is located on a small island in the North Eastern corner of the world map.