How does an application launcher update itself?

Question

Launchers are most common in games. Think of League of Legends, Starcraft II, or almost any MMO out there. Before starting the actual game, you have a small launcher app that takes care of updates and patching.

I want to move this direction with a particular non-game application I am developing. The concept of the launcher makes perfect sense: it checks for updates, replaces the appropriate binaries/libraries, maybe runs an integrity check, and launches the application. However, how do launchers update themselves? This tends to be a rare event, but how is it done? Does the launcher literally just write over the very binary it is currently running from? Or is there some kind of swap step after the download? I need to be able to push out (rare) updates to the launcher (especially if I discover some bug in my launcher).

My particular project will be in C#, but I am interested in conceptually similar C++ and/or Java solutions as well for future reference.