If you AirDrop something to yourself, like a photo from your iPhone to your Mac (see below), you won't see an option to Accept or Decline – it'll be automatically sent to your device. App links open in the App Store, so you can download or purchase them on your own device. For example, photos appear in the Photos app and websites open in Safari.
If you tap Accept, the AirDrop will come through within the same app it was sent from.