Model number starts with ( N )

• If the model number starts with M, it was purchased new from Apple.
• If the model number starts with F, it was refurbished by Apple or a carrier.
• If the model number starts with P, it was sold as a personalized iPhone with an engraving.
• If the model number starts with N, Apple provided it as a replacement device for a malfunctioning iPhone.

That's a service replacement. It could be for any number of reasons including replacing a damaged device, warranty replacement, or even just in lieu of providing a normal service repair like a battery replacement or front screen assembly fix. They come in a white box without any graphics (i.e. an image of the device), can be new or refurbished, and will have no accessories in the box. I believe that all refurbs (including replacement devices) have a new battery.

There's probably no way to tell if it's new or a refurb unless it's possible to find the history of the serial number. Not sure if the serial number is changed when a device is remanufactured into a replacement device. Maybe if right out the box it's possible to look at it carefully for any wear. Every Apple device I've owned was pristine out of the retail box, but can supposedly have some cosmetic wear if refurbished. Even then some of refurbs could be returns that barely have any wear.