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I'm not disagreeing with you two, just asking for details.
It may or may not be extremely dark, but the most notable attribute will undoubtedly be the smell. Burnt gear oil smells, well . . . unmistakeable. Most all tranny/diff gear oils typically smell, but when they get burnt, it's just god awful.
Under normal conditions, the additives (like sulfur- pee-yoo!) contained in the oil will react with tiny particles of iron wearing off the gears and cause a harmless discoloration. When it all get cooked real good though, the smell becomes greatly intensified, to the point that once you smell it you'll likely not forget it, and whatever you do - do not spill the stuff anywhere that you don't want to be smelling it for the next few months.
Normally, both gearbox lube or diff fluid will be a honey colored. The diff fluid does use pressure additives that smell like sulfur, but burned diff fluid will look darker, almost a black color, and you can smell a burnt quality to it.