You have to check the activityactions table for the same.In case condition in that table met then SM will not ask for update and a historic activity record will be created.
Check forum for same.
Whenever you update a record activities are logged for conditions defined in activityactions table and update you put in updatefield. In case you check that box : After save if condition of activities(as per activityactions table) are met then activity record will be created else you would be prompted to provide update so that at-least one activity could be logged. In case you unchecked : It does not matter whether activity is registered or not no prompt will be there for activity.
As per help of this box:"If selected (set to true), requires the operator to enter an update, if one or more activity records are being generated." Means if you want to capture atleast one activity for any update then you have to check the box.
So unchecking the box will not prompt you for activity but you have to ensure that important modification to change record should be tracked.
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