Yes, unsettling as it is, dark grey/black paste on drain plugs and diff internals is pretty common.
I changed the oil in my 2005 S2000's diff. Car was owned by a middle aged woman that drove it less than 3,000 miles per year and kept it garaged. Oil (factory fill I presume) had less than 15,000 miles on it. The crud inside this thing was pretty bad ... took me a while to clean the plug.
I plan a quick interval with the Chevron ESI 80W-90 of about 1 year's use (expect 3,000-5,000 miles) then I'll dump it and refill with the same for an interval about triple that. Hopefully the Chevron will clean out some of the gooey paste that's in there and it'll come out with the next drain.
If I can get an interval of 12,000+ miles on the diff oil, I'll do a UOA.
I'm pretty leery of using solvents to clean parts in a diff ... unless I am able to allow a day or so of drying to remove any and all traces of the cleaner before diff cover goes back on and new oil goes in.