The common definition of a dry-to-dry processor, is a Roller-Transport processor that has a washing unit and a drying unit attached, or built-in, so the RC paper comes out dry and finished. Such processors may have built-in chemical replenishment pumps, and are almost certainly always plumbed into water and drain pipes. I have a Nutek ACP 500 with attached wash/dry module myself. With it I have developed thousands of sheets over the years of RA-4 color paper. Some, like my Nutek, have variable speeds and variable thermostatic temperature control, so you can set them up for various processes, from B/W RC paper,. to RA-4 paper, to Ilfochrome paper. In every case, they only do "RC" papers. The common Fuji Frontier mini-lab processor found in may Wal-marts is a dry-to-dry processor, with additions like print trimming to size, and even has the built-in laser exposure unit on the front end.
Common brands found used in potentially dry-to-dry print processors, for color would be Durst, Nutek, Fujimoto, Hunt, Kreonite and others. In b/w RC dry-to-dry processors there have been units from Kodak and Ilford.