Jailbreaking, Rooting, and Sideloading

Sideloading: Installing an app from a different source than the official app store.

This can be achieved on an Android by enabling the setting.

To do this on an iPhone requires that the device is jailbroken. 

Jailbreaking / Rooting

These methods are used to gain elevated privileges to system files on mobile devices. MDM (Mobile Device Management) can prevent this.

Jailbreaking: iOS (iPad, iPhone)

Rooting: Android