And since I was thinking about trying that free Android app (I never install an app without knowing its provenance - and this is clearly a field ripe for ripoffs) I found this in a post by its author:

You seem to be mixing up a few apps that have different limitations and purposes. OpenSong, OpenSongApp, OnSong

• OpenSongApp is me. It's an open source application (anyone can contribute). It only works on Android. It is designed to help users of the great desktop application 'OpenSong'
  
• OpenSong', probably the most widely used, available on Windows, Mac, Linux, but not mobile devices, is also OpenSource (anyone can contribute to and help develop the coding) - something I've done in the past. A great team of developers! I have not copied them, I've written a stand alone application that allows users who already have songs in this application, to display them on a mobile device for performing. OpenSong concentrates on projecting words for congregational singing and managing a collection of songs (with or without chords).
• OnSong is an iOS only application that acts like a song book - like mine and hundreds of others out there. If you own an iOS device, it seems to be the go to app, suggesting it is very good. I've never owned an iOS device and was completely unaware of this app when I started developing mine - which I wrote to help me learn Android programming and to give me a song book for my tablet - at that time, I couldn't find an app that did what I needed on Android. I've still never actually used OnSong (although I regularly work with users who do), so I can't comment on how it works or its features, or indeed its similarity or not to mine, but I've taken time to get the apps to play nicely with each other.

(Ref)