When cats are washing themselves, are they "doing the laundry", or "taking a bath/shower"?

Yes for both.

Neither. By essentially aligning the hairs in the most aerodynamic way possible, they are preparing themselves for efficient feline ninja tactics which will help with the plans for world domination.

Taking a (spit) bath.

They’re taking a bath and using their spiky little pink tongues to rid their fur of dust, mites, excess hairs, etc.

Making themselves even more perfect than they already were.

Whatever they are doing, it is not a very good job. It’s mostly superficial just for show. The real dirt is down deep close to and on the skin.

@gondwanalon https://makropp.files.wordpress.com/2018/04/disapproving-cat.jpg