Thanks. Turns out, after some more digging, that it was part of what I owed for the year but was categorized as an "extension" payment (since I filed an extension - first time ever, actually.) The amount I paid was what was calculated to be paid as the usual annual tax payment, and the $2016 was to be paid with a different stub as the "extension payment." Having never been in this position before, I didn't notice that part.
So now I have to pay it plus interest and penalty.
Lesson learned.
