In case an object is to be sold voluntarily, the valuation of the object depends on the sales mode of choice:
The value for private sale is the figure that would be obtained when an object is voluntarily offered for sale in a usual way under the best circumstances, not taking into account charges of auction or trade - based on a 'willing buyer - willing seller' situation.
The value at auction is the amount that an object would generate at voluntary public sale or auction after the best possible preparation and circumstances.