The AI has three basic types of wars when it is the agressor:
(1) total war
(2) limited war
(3) dogpile war
(1) total war means the AI is more or less trying to take as many cities as possible, and going all out
(2) limited war means pillaging is more likely, less overall production will be going to the war effort, and also means the AI will charge less for peace. While still focused at taking cities, it is not so much the primary goal.
(3) dogpile war means the AI went to war when someone else was already at war, adding in to attack a weak opponent. In such a war, an AI will seek peace if the others at war also seek peace, not wanting to stay in a war without one's allies.
The final type of war is a defensive war (when someone else declared war on the AI).
The type of war affects both the production choices of an AI and also the price for peace.
-Iustus