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 the three names still blur together after that, Gestoraz covers the same ground in more detail, and one calm read tends to settle the question for good.
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.