What's the difference between Activity.runOnUiThread(runnable action) and Handler.post()?

Activity.runOnUiThread, like it's name implies, will execute the Runnable in the thread that is currently responsible for the UI. So, if you have a CPU intensive task, it can make the UI unresponsive for a short period of time. Conversely, Handler provides a way for you to create a thread, run some code, and notify the UI when you are done (i.e Handler.sendMessage).

The docs for Handler state this better than I can:

When a process is created for your application, its main thread is dedicated to running a message queue that takes care of managing the top-level application objects (activities, broadcast receivers, etc) and any windows they create. You can create your own threads, and communicate back with the main application thread through a Handler. This is done by calling the same post or sendMessage methods as before, but from your new thread. The given Runnable or Message will than be scheduled in the Handler's message queue and processed when appropriate.