The authors agree that this surname derives from the given name Terzo, given to the third child, with roots in the Latin cognomen Tertius. E. De Felice notes that in some cases the origin may be toponymic, from localities called Terzo —among them Terzo d'Aquileia, in the Udine area— and other places with that name in different provinces of Italy. E. Rossoni mentions specifically the Borgo di Terzo, in the Bergamo area, and documents the transformation into a surname in that area around the 16th century and in Borgo di Terzo around the 18th century.

As for geographical distribution, the authors agree that the variant Terzi is concentrated in northern Italy, particularly in Lombardy and Emilia-Romagna. De Felice adds that the form Terzo is typical of western Sicily. Rossoni specifies that Terzo has its main nucleus in Sicily, with a presence also in Naples and in the Vicenza area; and that Terzoni has a nucleus in the Piacenza area and another in the Macerata area. De Felice also records the variants Terzulli, typical of southern Italy, and Terzani, typical of Tuscany.