I think it is NIE. My place of work is organizing the paperwork for my job. Maybe I will ask them about NIE as I need a car apon arrival in Spain. Thank you for answering my thread. I will get back to you about this.
If you are going to be working in Spain then you will, necessarily, be resident in Spain. As such, you will need to sign on the list of foreigners and get your green certificate (aka residencia).
You are correct that your employers only need an NIE but you will need to go that extra step. This is best done when you are working and have your contract of employment. With this, it is so much easier to prove income and prove that you have health provision.