OnSong supports external video modes that allow for full-screen lyrics projection, or for use as stage video monitors. If you are seeing the screen of the iPad instead of one of these modes, there are two likely reasons:
Generic Video Adapters
If you are using a wired connection to your video device, you will need to make sure you are using an Apple-branded adapter. Generic video adapters are only able to mirror the screen as it appears on your iOS device. Keep in mind that some retailers on websites like Amazon may promise the adapter's origin is Apple but maybe a cheaper knockoff. We recommend purchasing directly from Apple for these products.
Here is a list of adapters that iOS supports for second screen capability: http://onsongapp.com/docs/features/external-video/devices/
iOS Screen Mirroring
By default, OnSong is configured to project lyrics. You can change this to stage monitor mode using the External Video Menu and tapping on the fifth icon (on the right, which shows a graphic of a device connected to a screen) below the preview to enable Stage Monitor Mode. However, there is a third mode that OnSong can use which, in effect, turns off OnSong's control of the second screen resulting in the default iOS behavior to mirror the content on the iOS device's screen. You may have inadvertently enabled this setting.
To toggle iOS screen mirroring, tap on the gears icon in the Menubar to open the Utilities Menu. Next, tap on the Settings option and then choose Live Settings on the left and External Video on the right. You will see an iOS Screen Mirroring option. If the screen is currently mirrored on the connected video device, make sure this is turned off. Likewise, if you want to enable screen mirroring for training purposes or tutorial video capture, turn this option on. Once you tap Done, you may need to Restart OnSong when switching these modes.