There are several, here are the enums and a brief description in my own words for what they do
NO_WARPLAN
This happens with unexpected wars, most commonly this would be a vassal or ally getting pulled into a war. Typically however this means the AI isn't at war as once they get pulled into an unexpected war they should define a war plan very quickly.
WARPLAN_ATTACKED_RECENT
This is used for new defensive wars and quickly replaced with the next one.
WARPLAN_ATTACKED
Defensive war plan, obviously.
WARPLAN_PREPARING_LIMITED
Building up for a limited war against an enemy. This mainly involves changing production and relocating units.
WARPLAN_PREPARING_TOTAL
Same as above for total (large scale offensive) war.
WARPLAN_LIMITED
Engaged in a limited war.
WARPLAN_TOTAL
Engage in a total war.
WARPLAN_DOGPILE
Dogpiles are acts of opprtunity by the AI so there is no preparation plan.
In each case the exact effects mainly involve research & production emphasis and moving units. When at war or preparing for war the AI can switch priority over for techs based on the advisor setting. Production will shift to units and/or military/defensive buildings. I know this is a bit vague because there isn't a straight answer that applies to every leader. The warplan in effect will not always mean the same units/buildings will be produced by different leaders, it's only an influence. For instance most leaders will be encouraged to build units with UNITAI_PILLAGE when in or preparing for a limit war but it doesn't mean they will always build more of them.
Hope that helps even if it is a bit vague
Edit: I should also add that the AI doesn't only evaluate their own war plan, they also evaluate the other AI war plans. This is another use of NO_WARPLAN where one civ will count the number of war plans, excluding NO_WARPLAN, that other civs have active.