E. Rossoni links this surname to the medieval name Candius, documented in a 17th-century text. According to Rossoni, the surname Candi is distributed in the Parma, Modena, Bologna and Ferrara area (Emilia-Romagna), as well as in the Ancona area (the Marche) and in the Rome area (Lazio). The form Candio, on the other hand, appears in the Verona and Vicenza area (Veneto), in Rome and in the Bari and Lecce area (Puglia).

V. Blunda proposes a different etymology for the Sicilian variant: it would derive from the Arabic term qandi, meaning "rock candy". Blunda recalls that sugar was introduced into Europe by the Arabs through Sicily during the period of the Emirate (827–1091), and that this Arabic word gave rise to both the Italian and the Spanish "cande" and "caña". This hypothesis suggests an independent origin of the surname in Sicily, without relation to the medieval Candius noted by Rossoni.

The surname therefore presents at least two independent clusters of origin, arisen in different regions without direct relation to each other: one linked to northern and central Italy from a medieval personal name, and another of Arabic root peculiar to Sicily.