We consider evolutoids and pedaloids of curves and frontals in the Minkowski plane. Firstly, we present the families of curves by using the pedals and evolutes of regular curves. We investigate the relationships between these families of curves, which are called evolutoids and pedaloids. Also, defining the notion of contrapedaloids, we investigate the similarity in relationships for them. Then, we generalize these notions to frontals by using their moving frame since the evolutoid or pedaloid is not defined as classical way for curves with singular points. Finally, we give examples that confirm our results.