It will be new, or “remanufactured” - a bit different than refurbished; remans always have all-new exterior (including display) and battery. Only circuit boards & electronics are potentially harvested from prior use.
Either way, it’ll come in a plain white box & it’ll have a new serial so you won’t only not know if it’s new or reman, there’s really no way to tell. And yes, it will definitely be the model you sent in & not a 15.