I was on a Trident sub and yes, we had porcelin toilets that worked like regular ones. They went to tanks and we pumped the sanitary tanks. There were dirty sans, (toilets, kitchen drains) and clean sans (bathroom and shower drains).
The TDU (trash disposal unit) job was the worst on the boat. The hydraulic compactor would normally squeeze the liquid from a dirty paper towel or kim wipe all over the floor. I'll tell you about the legend of the Mad Shitter later.
I have *yet* to hear of a Navy vessel that wasn't plagued by a Mad Shitter. That, and a ship in dry dock that didn't have a Firebug.