I myself like to call a Jeep a Jeep and will always refer to our Jeep as a Jeep no matter what mods it has on....
I'm in this camp. "Jeep" carries the aura and mystery of the "Jeep Thing" that rig does not.
But anytime you move away from stock, in my book you have modified or rigged your Jeep, even if it's grab handles and mats. Call it a rig if it suits you. Just doesn't work for me as well as "Jeep".
2013 JKR, Auto, Yukon 4.56, Nitto Trail Grappler 35/12.5/17 on XD222 KMC Enduro Beadlocks,Teraflex Big Brakes & Spare Carrier, Warn RC Winch, Metalcloak Front & Rear Bumpers, Metalcloak Overliner Flares & Front Inner Fenders w/ Corner Guards/Tail Lamps, Metalcloak Game Changer 2.5" w/6-Pac's, ARB Diff Covers & Onboard Air, AFE High Tuck Muffler, Front Lower Control Arm Skids, Artec Aluminum Skid System, Poison Spyder Hood Vents, Ripp SC.
There are no winners here; just beguiled participants