As far as I can see the results seem identical in both Render view and when rendering in MPlay.
Can any Houdini experts explain the differences between the 2 rendering methods and when to use each?

Mplay is just a viewer, you can render multiple images to it and scrub through them, save files etc.
http://www.sidefx.com/docs/houdini15.5/mplay/_index [sidefx.com]