Anne,
State = Tells you if the Project (or other work item) is in a state of Draft, Active, On Hold, Cancelled or Completed. The field cannot be changed through the column. You need to change it through the Mark As button on the Ribbon Toolbar (i.e. Mark As Active).
Status = We monitor the status of a work item. If it is not Active then it will be Not Active just like State. If the work item State is Active then it will be On Track. If there is no work done on the tasks according to the work and duration specified, this status may change to At Risk or even Off Track if the status cannot be recovered to On Track within the allocated timeline. For example, if a Task is still active after the Due Date has past, the Task will show red 'Off Track' because the task cannot recover back to On Track (unless the Due date is manually changed). At Risk is a bit tricky. It is based on how much work on a daily basis the resource puts in.
Example - If you have Task with 5 day Duration and 10 hours of Work. The system expects the Resource to put in 2 hrs of work per day. If that requirement is not met after the first day, the Task will change to AT RISK. If the Resource puts in 4 hours on the second day, which technically catches them up, then the status will change back to ON TRACK.
Hope this makes sense.
Sincerely,
Boris