App Store Distribution Provisioning Profile vs Development Provisioning Profile

The development profile serves for developing and testing on your devices.

The distribution profile serves for making your IPA file, sign it and send it to Apple.

It is clearly marked that you cannot run it on devices, unless you have an Ad Hoc distribution profile:

App Store provisioning profiles do not allow for a distribution built application to be installed on an Apple device. To install your distribution ready application on a device, you must create an Ad Hoc provisioning profile.

Back in 2014 when this question was asked, and perhaps a bit later, it was perfectly possible to install an application signed with an AppStore profile on device, provided that the matching AdHoc profile was already installed. This subsequently changed, and it is no longer possible (2019) to install an app signed with an AppStore profile except via download from Apple (e.g. via TestFlight).