Normal Battles - typically 5 Stamina usage
Battles or missions that do not progress the game story. However they do offer experience and gold for victories as well as the ability to get items from defeated units. You may want review the armies in these battles to determine the chance of you seeking certain items.
Some of these battles may be hidden when a daily quest or battle is started. They will reappear when that quest is over.
Daily Battles - typically 7 (or 8) Stamina usage
These are normal battles that are offered in each town with a certain goal. Completion of the goal will result in a reward that is collected. Typically daily quests are done to get common units. They are called daily battles because once all of the goals are completed, it typically takes 12 or more hours for the next time you can get that reward again. Such quests can be started by talking to the leader of each town and accepting their quest. Once started, some of the towns normal battles will be replaced.