A plain account of the number, the green certificate and the residence card, with the muddle taken out.
The NIE is the number. EU nationals receive a green certificate; everyone from outside the EU receives a TIE card. All three end up, confusingly, being called "the NIE".
If you are non-EU and settling on Lanzarote for the long haul, you will in the end need a TIE card that carries your NIE number.