When you are in a reader's page, you will see both a Log (lefthand navigation) and the Program Log under the title of the program.
The Log allows you to see all reading logged over time for that reader. It will include reading that both pre-dates and comes after the dates of your programs. This is the log for all time for that reader.
The Program Log only takes into account the reading, activities, and/or points that will count toward that specific program.
It is always wise to check the program log if a participant feels they should have enough reading/activities, etc. to have earned a badge or prize and have not yet earned it.