You can find the specifics at the API site, but generally the "+" came from greater soot control additives, IIRC. The CI-4 rating was short-lived, and quickly became the CI-4+. Here is the API quick read:
http://www.api.org/certification-programs/engine-oil-diesel-exhaust-fluid/~/media/Files/Certification/Engine-Oil-Diesel/Publications/MOM_GUIDE_ENGLISH_2013.pdf
Generally you can always "upgrade" to a higher level of API cert, but never "downgrade" from your OEM spec requirement.
Yes, you can most certainly safely use CJ-4 in your CTD. CJ-4 lubes generally have even more soot control and wear control, although much of that would depend upon individual engine traits and also fuel type used. Presuming you're on ULSD (as nearly everyone is) then the former fluids (with higher TBN) mean nothing today, and even then, shorter OCIs negate any of that former debate. Only the combination of greatly extended OCIs and the use of LSD fuel would make CJ-4 a concern over the former fluids.
There exists a plethora of used oil analysis here; you can search both the older and newer used oil analysis and see for yourself. CJ-4 is a fine fluid and offers excellent service. The initial fears of it being inferior due to different additive packages were completely unfounded; the doomsday predictions fell far short of reality.