Stats of the Chocobo

Physical
Strength affects the chocobo's running speed.
Endurance affects the chocobo's riding duration.

Physical
Discernment affects the chocobo's potential to learn abilities.
Receptivity affects the chocobo's ability to communicate with fellow chocobo.

Other Attributes
Energy is the power the chocobo needs to remain active. It also affects the success of care plans and the frequency of care options.
Affection is the most important part of chocobo raising. It greatly affects the success of care plans.
Satisfaction changes with feeding and affects energy recovery.

The Affects of Caring
The different types of care will modify your chocobo's stats. Not all types of care will be available right from the start, but as your chocobo grows, you should "unlock" new types of care.

Watching over the chocobo strengthens the bond of affection, and places very little stress on your chocobo.
Telling a story strengthens the bond of affection and trains mental faculties. Telling various stories may have a beneficial effect for the chocobo.
Scolding the chocobo disciplines the chocobo, but it slightly weakens the bonds of affection.
Competing against others strengthens the bonds of affection, but depletes stamina. However, it does entertain a bored chocobo.
Going on a walk strengthens bonds of affection, but depletes stamina. The chocobo might meet someone on its travels!

Care Plans
Care plans also affect your chocobo's stats. Square released the following chart to show the relationships of gains and losses for each care plan.