It seems pretty clear that there is still a lot of confusion regarding what is NIE and what is residencia, and what do they look like, so here you have a very simple way to differentiate them:
Lets put some examples, so you can understand me better. Imagine that you call your fridge "freezer". Both fridge and freezer are in the kitchen and have a similar roll, and you can even find them to be part of the same appliance. But a fridge is not a freezer, so even if you would like to call "freezer" the fridge it wont make it true that a fridge is a freezer.
Another example. In Spain we have our DNI (documento nacional de identidad) and our passport. Both documents show our ID number in them, and both can be used to identify yourself. But a DNI is NOT a passport.
It is the same with NIE certificate and residencia documents.
This is the NIE certificate:
And these are the current EU residencia documents. The big green A4 is not longer issued but it is still valid.
The green old residencia A4 document is NOT a NIE certificate, it is your residencia paperwork. NIE literally stands for Número de Identificación de Extranjero (foreign ID number), and it is simply a number that identifies you within the Spanish system.
Having NIE does not mean that you are resident. You are only resident if you have registered with the national police as foreigner living in Spain. They then give you a document commonly known as "green residencia card", which before the current small green card size document it was a green A4 page.
The residencia card and the green A4 both quote the NIE number, as it is the number that identifies you within the system. But if you check your small green residencia card you will notice that at the back of the card (the laminated part of the card) has a number. That is your residencia card number, and it links the information that it is hold about you in the front of the card with the application that you submitted with the police. And this is why is laminated and why when you are asked to present a copy of your residencia card, you need to photocopy both the front and the back.
Therefore, on your card you have your residencia card number and your NIE number, same as in our ID cards, where we have the ID number and the ID card number, which are not the same. The old green A4 document also has a residencia number, which is located at the top of the page on the right hand corner.
If you are asked to prove that you have a NIE, you can either show your NIE certificate or one of your residencia documents (green A4 or small green card), but if you are asked to prove that you are resident you wont be able to do it if you only have your NIE certificate.
This is the old residencia plastic card with picture, which is not longer valid, and you if never renewed it you will not be considered resident anymore.
And finally, this is the TIE (Tarjeta de Identidad de Extranjero), which is the residencia plastic card for non EU citizens. Once the implementation period is over, British citizens will have to exchange their current EU residencia documents for this TIE, or to apply directly for it if you have not gained residencia before the end of the implementation period.