The Romans were part of the Latins--traditionally consisting of 30 peoples (there was a myth of a sow giving birth to 30 piglets representing the 30 Latin peoples). Until 338 Rome was a member of the Latin League which fought frequent wars against neighboring tribes (Sabines, Volscians, Aequi, Hernici, etc.). In 338 Rome fought a war against the Latins, defeated them, made some of the Latins Roman citizens and kept the rest as Latin allies.
Rome had always been the most important of the city-states in Latium. Among the others were Tibur (Tivoli) and Praeneste (Palestrina). The modern-day region of Lazio in Italy includes ancient Latium but also land on the north side of the Tiber River that was part of ancient Etruria.