What is the difference?

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I'm not sure, but I think "Application Complete" means that they've received all your app materials (or finally verified that they have it all). I think "Under Review" means that they are now actually looking at your app (rather than having it completed but just sitting somewhere).
 
see i thought the same thing...I just had one that changed from "under review" to "complete". I must be going backwards in the selection process... next thing you know they will send me a check for the secondary 🙂