One connection between both characters is that they are part of the gang that initially kidnaps Buttercup. The Sicilian is Vizzini. He operates as the "brains" of the operation, as he is extremely cunning and deceptive. Inigo is the classical swashbuckling swordsman who mourns the death of his father. In his forlorn state, he follows Vizzini because his one focus is avenging his father's death that came at the hands of a "six fingered" man. The connection between the Siciian and Inigo is that they are both part of thew same gang.
Another connection between them is that they are both bested by the Dread Pilate, who is actually Westley. He is able to best Inigo in fighting him in a sword match. Inigo is fundamentally impressed that the masked man has been able to best him in such a thorough manner. Inigo ends up becoming indebted to the masked man, as he is left alive as an honorable gesture. Vizzini is also bested by the masked man in a war of wits as to which chalice was poisoned. In this, another connection between the Sicilian and Inigo is evident in that both of them are confronted and lose to Westley.