Yes, much to my frustration, the reporters and even GeneralFanager and CapFriendly appear to get this wrong with their terminology. Tawnos and I both looked into this, and it seems pretty clear that you can have either a NMC or a NTC, and either one can be modified, typically to allow for limited trading.
The difference is that with a NTC, you can still be demoted, waived, exposed to an expansion draft, etc. regardless of whether it is "full" or modified. With a NMC, you CANNOT be demoted, waived, exposed to an expansion draft, etc., even if it is modified to allow for some form of trading. (Interestingly, however, the various sites ALSO show listings for M-NMC, which leads me to believe that there may be modified versions of NMCs that allow for, say, waiving, but not demoting - though I should point out that I don't actually know this for a fact, and am only offering conjecture on this point.)
The problem is that these knuckleheads reporting on the contractual details for some reason have difficulty understanding the basic structural differences above and insist on mangling a NMC that allows for limited trading by calling it a "full NMC with a limited NTC" or variations thereof.
We'll never know for certain without seeing the actual paperwork, but after wading through how the sites list him plus all the various reports in the press (and then using basic deductive reasoning) it seems pretty clear that what Girardi has is a full NMC in the first three years of his contract and then becomes modified to allow for limited trades (but still prevents him from being demoted, waived or exposed to expansion) in the last three years.
The interesting thing is that Staal's contract continues to be listed as a full NMC in the first three years and then a modified NTC in the last three. I wouldn't be surprised at all if we learn sometime in the next year or two that GeneralFanager/CapFriendly made the same mistake with him...