For me it is what was called a "Sloppy Joe" in Bernards Township in north New Jersey and specifically in a small Deli on the southwest corner of the downtown square in Basking Ridge, NJ, and it bears no resemblance to the gooey ground beef concoction that most people call a Sloppy Joe. It is though currently sold as the "New Jersey Sloppy Joe" on a couple of SoCal college campuses.
It consists of two Sour Dough or Rye bread slices layered on both sides with liberal dose of Russian or Thousand Island dressing, then an 1/8lb+ layer of sliced beef, ham, and turkey, and then three slices of cheddar, swiss, and colby cheese, and finally topped with a finely chopped cole slaw.
It's simple yet complex, and just plain full flavored. I still make then at home 30 years later, but they never taste quite the same as that little deli in NJ.