Essentially the Rivet Joint aircraft collect communications signals from the electromagnetic (EM) spectrum for signals intelligence and the Combat Sent collect radar specific signals emitted on the EM spectrum.
An RC-135 Rivet Joint aircraft from the 9th Strategic Reconnaissance Wing approaching—USAF photo
An RC-135 Rivet Joint, with its 34 member crew, flying Afghanistan skies—U.S. Air Force photo/MSgt. Scott Wagers
Captains Guy Perrow (pilot) and Erik Dunkley (copilot) and 1st Lt. Michael Morrison (navigator) prepping their RC-135 Rivet Joint flight—U.S. Air Force photo/MSgt. Scott Wagers
Electronic warfare officers (2 of the 34 member crew) Lt. Col. Doug Sachs and 1st Lt. Beth Brockshus monitoring sensors scanning the Earth’s surface to detect, identify and geolocate signals throughout the electromagnetic spectrum on board their RC-135 Rivet Joint—U.S. Air Force photo/MSgt. Scott Wagers
Staff Sgt. John Terlaje and Airman 1st Class Ross Vandenbosch towing an RC-135 Rivet Joint reconnaissance aircraft and showing the antennae panels on each fuselage side—U.S. Air Force photo/MSgt. Scott Wagers
The RC-135U Combat Sent with its 23 person crew—U.S. Air Force photo
Another view of a flying RC-135 Rivet Joint clearly showing the plethora of antennae both on the wings as well as fuselage—USAF photo