A jargon-free walk through the number, the green slip and the residence card — and who gets which.
The NIE is the number, full stop. EU citizens receive a green certificate; non-EU citizens receive a TIE card. All three get lumped together as "the NIE" in everyday island talk, which is where the confusion breeds.
If you are non-EU and putting down roots on Ibiza for the long haul, the document you ultimately need is a TIE card with your NIE number printed on it. Sort out which camp you fall into early and the rest gets simpler.