So this is a bit confusing because "Latin" was an ethnicity, and also a legal status. "Roman" something like an ethnicity, and a legal status. This confusion arises from the different ideas of citizenship the people in the ancient Mediterranean had.

First, Rome was Latin, in the sense that it's located in Latium, its majority language was Latin, its people participated in cults associated with the other Latin speakers in the area, like the cult of Diana at Aricia.

Now, citizenship could be more or less open, which in turn would stress a greater or lesser separation from the wider ethnic group. You could, as Athens at some points, require citizens to be only the descendants of citizens. That approach stresses the separation from the larger group and makes interbreeding and immigration difficult. In Athens' case, by the Classical period, although Athenians considered themselves relatives of the Ionians, their language had become recognizably different (Ionian is taught as a separate dialect). Claims to ethnic solidarity with Ionians could sometimes still pop up, but it wasn't a particularly tight relationship.

Rome usually had a more open model of citizenship (although by Hadrian they had made laws restricting citizenship to those born to Roman parents - "Roman" by that time had become a very different thing from the early Republic). Rome adopted from time to time whole communities as Roman, and individuals for some service to the state, and recognized Latins as closely enough related to Romans that, if the Latins relocated to Rome, they could gain the citizenship. By keeping this more open attitude toward citizenship, Rome remained more closely related to the other Latin states.

As Rome developed its treaty system in the Italian peninsula, the special relationship Rome had with the Latin cities became codified as the "Latin Name" or "Latin Right," a specific set of legal rights Latin communities had in relation to Rome - that could be granted to ethnically non-Latin people. "Roman" at the same time picked up more of a legal sense to it.

That's not to say the ethnic component of "Roman" was stamped out; for instance after the Social War of 90-89 BCE, when Rome enrolled almost the whole Italian peninsula as Roman citizens, we hear of riots in the forum over how to distribute the "new" citizens across the 35 Roman voting tribes - the "old" Romans wanted to restrict them to 10 new tribes, limiting their ability to influence the voting assembly, and the "new" citizens wanted wider distribution. It's interesting to note that Appian, the source here, can only find the words "old" and "new" to distinguish between these groups. He seems to have a hard time understanding "Roman" as an ethnic term that might let him talk about "real" Romans or somehow otherwise marginalize the new citizens.

A bibliography on all this would be quite long. I think Sherwin-White, The Roman Citizenship, is still the standard work on the Roman citizenship, although being quite old by now. Farney's Ethnic Identity book might be important too, though it is more pointed toward the Late Republic and early Empire. You can find various regional histories like Williams' Beyond the Rubicon, which looks at Cisalpine Gaul, though i don't know one off the top of my head for Latium.