Over the years, several classes of scalarization techniques in optimization have been introduced and employed in deriving separation theorems, optimality conditions and algorithms. In this paper, we study the relationships between some of those classes in the sense of inclusion. We focus on three types of scalarizing functionals (by Hiriart-Urruty, Drummond and Svaiter, Gerstewitz) and completely determine their relationships. In particular, it is shown that the class of the functionals by Gerstewitz is minimal in this sense. Furthermore, we define a new (and larger) class of scalarizing functionals that are not necessarily convex, but rather quasidifferentiable and positively homogeneous. We show that our results are connected with certain set relations in set optimization.