Agreed Value: Indicates that the property covered by the applicable coverage will be settled based on a property value agreed to between the insurance company and the insured. For example if Agreed Value is selected for collision on a 1936 Fire Truck that is difficult or impossible to replace (i.e. a value may be difficult to determine based on the rare nature of the property) then the insurance company and insured may agree to a unit value of $20,000. Then in the event of a total loss the insurance would pay out $20,000 (i.e. the Agreed Value).
Stated Amount: Indicates that the property covered by the applicable coverage will be settled based on a property value as stated on the policy or Actual Cash Value, whichever is less. For example Stated Amount is selected for collision on a unit and is stated to be $85,000. The cost to replace the unit new would be $200,000 and that unit has depreciated 50% then in the event of a total loss the insurance would pay out $85,000 (i.e. the $200,000 replacement cost multiplied by .5 is $100,000 but the Stated Amount is $85,000 which is less).
See policy forms for full details.