That is entirely handled by each mobile touch device.
There is normally special code to make touching somewhat equivalent to clicking, but it is still not consistent and well done over many devices. If you switch among different WordPress themes (including the default Twenty series), you’ll see quite different behavior among them on touch devices. (This includes Windows desktop/notebook touch screens.)
Windows 8 does seem to know how to handle both a mouse and touching, but I don’t actually have a test platform to verify that. The latest Weave Xreme 1.1.2 has new code to work better on Windows touch screens. So some of it is indeed having correct software on the site/theme side, and it isn’t all the OS/Browser.
I also have not ever tried a physical mouse on an Android or iOS, so I will add that to the list of things to check out – if possible.
I would suspect that in the worst case that clicking by a mouse would be treated just like a touch, but I don’t know for sure.