I am developing an app that runs on Android/iOS and desktop computers.
Should I use the click or the tap event?
What are the differences between them?
Will the 'tap' work on desktop? if not, (and I have to use click) am I missing any advantages that the tap has over the click?
Touch events and mouse events are entirely different beasts. They are not interchangeable.
That said, I'm using jQuery Touch Punch which maps touch events to their mouse event analogs, so a tap becomes the same thing as a click. This makes it possibly to use all the standard jQuery UI goodness without having to do any special touch event programming. It's extremely simple to use, and so far has worked perfectly for me on both iDevices and Android.