Why is my Position Tracking Visibility Score a different number on the Projects dashboard than it is when I go into the Project?

If you apply the filter to turn off "local pack" results in a Position Tracking campaign, it will be reflected in the Position Tracking tool’s Overview report and the Visibility score of your campaign will be adjusted. 

However, the Visibility score seen in the preview widget on the Projects dashboard will always represent the visibility of your domain including local pack results.

So, inside the Project the score will adjust if your settings say to exclude local pack results, but the score on the Projects dashboard will always show your visibility including local pack results.