In the late Republic, laws - leges in Latin - had to be passed in the Tribal assembly, in which every Roman citizen had a vote. It was not, however, a direct democracy. The Tribal assembly was organized along the lines of the 35 Roman tribes, with each tribe getting one vote. These tribes acted in some ways like the American electoral college, where in most states the candidate that gets 50%+1 of the vote is considered to have won all the electoral votes of that state. The tribes voted one by one, with the result of each vote announced immediately after it was counted. The number of participating members in each tribe could vary drastically, so that if few members of your tribe showed up (perhaps because you came from one of the 31 rural tribes and few members were in Rome for the vote), your individual vote could carry many times the weight of a member of one of the four urban tribes, whose members mostly lived in the city.

A plebiscite - plebiscitum - was something passed in the Plebeian council that had the force of law. The Plebeian council operated the same way the Tribal assembly operated. There are certain youtubers that claim this assembly really operated on a direct democracy model, without consideration of the 35 tribes, but Lily Ross Taylor (whose book Roman Voting Assemblies is the classic study) says nothing of the sort, and actively describes the Plebeian council voting in tribes. DON'T GET HISTORY FROM YOUTUBE! The real difference between the Tribal and Plebeian is that a consul or praetor runs... administers... chairs? It's early and I can't think of the word. Anyway, one of those two magistrate runs the Tribal assembly and patricians can participate, while a tribune of the plebs runs the plebeian council, and patricians were excluded.

The Centuriate assembly and the Tribal assembly both elected magistrates (the Centuriate assembly voting in centuries instead of tribes - that is, the Roman people in its military capacity), and the Plebeian council elected tribunes, who were not strictly speaking magistrates, though in many ways they came to be treated like one. Magistrates could propose laws, but did not act as a representative legislative body analogous to the US Congress.

The Roman organization that came closest to that kind of representative legislature was the Senate. Usually (not always) one got into the Senate by winning an election for quaestor or tribune, rather than winning an election for Senator. The Senate was made up (usually) of former magistrates, and members were (usually) members for life. The Senate could not pass laws - leges - but instead could pass a decree of the Senate - senatus consultum - which strictly speaking is advice for the magistrates. In practice it was advice that was very hard to ignore.