What is the proper term for real oil vs. flavoured oil?
Chilli oil has at least touched chillies (or chilli extract). Pizza oil on the other hand is neither made from pressed pizzas nor flavoured with pizza extract.  

English isn't logical. French isn't either, but at least it would use Huile de pépins de raisin, huile (aromatisée) au piment fort (or more commonly huile pimentée or huile piquant) and huile pour pizza, i.e. oil of, (flavoured) with, or  for something.