Battle's/challenge battle's are where you lead you armies against an enemy army and can range from defeating Ghost armies to fighting Giants or unseelie warriors.
Diplomancy Quests involve giving gold or food and selecting the desired outcome from a list provided and adding food till it's full, you may also be able to trade ladies and artifacts which is a good way of getting rid of unwanted ladies and artifacts.
Knight Recruitment quests can be Adventure or Diplomatic Quests. Knights can be invited to Join the Round table by paying for their services in Diplomacy Quest or rescuing them as is the case of Sir Bors and Sir Percivale in Advenute Quests. Knights can also be Recruited in Adventure Quests by completing tasks or following a certain storyline in the Adventure Quest as is the case of Sir Gawain and The Green Knight.
Advenute Quests are quests that follow a certain storyline and are mostly related to the story itself granting rewards like new knights or artifacts.
The Chance of battle is a possible outcome of quests and will be on the description of certain quests like random quests.