Direct Open
Occurs when a user opens your app by directly responding to a push notification by swiping or tapping on the notification.
Influenced Open
The number of opens that occur both directly and indirectly as a result of a push notification, minus the baseline opens that would be expected anyway. Every open that occurs soon after a push is a potential influenced open, whether it is the direct result of a push or not.
Some direct opens can occur long after the push was originally received. We attribute these to the relevant pushes; however, we don't believe they represent the same kind of influence. These are not considered potential influenced opens. Influenced opens are only calculated for a 12 hour window after the push was sent.
Depending on the app and the users, there may be some overlap of direct opens and influenced opens numbers. Neither is a strict subset of the other. To add the numbers together will give misleading results.