How can I save Keynote presentations as an auto-playing slideshow? In MS PowerPoint users can save their presentations as a PowerPoint Show instead of a PowerPoint Presentation. 

Besides changing the file extension from .pptx to .ppsx, this option means that upon opening the file it will automatically open in Slideshow mode rather than the typical PowerPoint editing mode. It also means the Slideshow can start playing automatically, so that it moves from slide to slide without user input (if it's been designed to do that).

Is there a similar feature in the Keynote app for macOS? If so, how do I use it?
The way this is done with Keynote is somewhat different to the PowerPoint approach.

Instead of having to save the presentation as a different file, you only need to change your presentation's settings within the Inspector.

Assuming you're talking about the latest version of Keynote on macOS, follow these steps:


Open your presentation in Keynote
Click on the Document icon at top right of the toolbar
Under Slideshow Settings, tick the Automatically play upon open checkbox
In the Presentation Type drop-down menu,  select Self-Playing
Now save your presentation


Now when you open it up it'll automatically play in presentation mode.

NOTE: Obviously you can play with these settings if you'd like to achieve a different outcome.