I try to learn topos theory from Johnstone's book referred to as the 'elephant'. So, by a topos I mean a cartesian closed category with subobject classifier.
Every Grothendieck topos is a topos. Every topos is a quasi-topos. So, for example, a result about quasi-topos may be applied to a topos or to a Grothendieck topos. I mention these facts as simple instances of precise relations between mathematical concepts.
What is the precise relation between $\infty$-topos and topos? (I am looking for a rigorous answer that in particular clarifies how the theory of $\infty$-topos may be applied to topos theory.)
Thnx.