Does an app downloaded on one device automatically show up another device using the same Apple ID?
If two devices have the same AppleID (typically what would happen if you have an iPhone and an iPad), then if an app is download on one device, it will change the icon in the App Store to show a cloud with an arrow rather then the "Get" or price button.

Additionally, depending on the iTunes &amp; App Store settings in the Settings app, the apps may automatically download to the other device.