Mechanic

The key between the two types (well, at least with US GAAP):

EXTRAORDINARY = unusual AND infrequent >> BELOW the line, NET of tax

NON-OPERATING = may be unusual OR infrequent >> ABOVE the line, reported GROSS (ie, bc tax is taken out after EBT)

In general, and borrowing from Uncle Becker, an income statement is like "IDEA":

I = Income >> Net Income, reported GROSS (EBT) and *then* NETted of tax (NI), in I/S
D = Discontinued Operations (NET of tax), in I/S
E = Extraordinary Items (NET of tax), in I/S
A = Accounting changes, in Statement of Retained Earnings (if it's an error/omission or change in principle, which require RETROspection and REstatement; changes in estimate are prospective, so that's only going forward and not reflected in past financials)