By the time of the social war the Romans and Italians were so intermingled that there was very little difference between them. And that's where the problems of the social war began.

Being a Roman citizen gave you special rights, the right to a trial, the right to not be killed without trial and everytime there was a problem between a Roman and Italian, guess which side the Roman courts took.

So prior to the social war the Italians were feeling pretty hard done by. They have their lives to protect Italy from Hannibal. They have their lives to save the country from the Cimbri during the Cimbrian wars, but at the end of the day they were second class citizens. They didn't want to leave the republic, they just wanted their fair share of Rome's pie, after all, they were dying in Rome's wars.

That's why as soon as Rome capitulated and gave out Roman citizenship, the war came to an end. The Italians had what they wanted.

In terms of culture and religion it was pretty much the same. There may have been different names for particular gods and different modes of worship but overall it was the Etruscan pantheon that was venerated.

There were language differences, most of the rebellious Italians spoke one or another sabellian language and the Etruscans (who did not rebel) spoke Etruscan. Most everyone probably spoke Latin or enough of it to get by. The elites were certainly fluent in it as well as Greek.

There was significant intermarriage among the elites of all the various tribes and romans. Culturally if a samnite married a Roman, etruscan, lucanian, bruttian they probably would not have any more surprised by anything they did than a Californian marrying a New Yorker.

The main problem was that romans had started getting particular about who they were letting become citizens. A hundred or so years before and non romans absorbed into the Roman state would have gotten citizenship with relative easy (look at the families of Marius, Pompey and Cicero) but by the social war it was a very guarded. The Italians felt, quite rightly, that they were being taxed equally to romans, served in the army equally to romans and suffered equally to romans (look at Jugurtha and Mithridates massacres of Italians) they should get equality under the law.

Some Romans agreed with this, there was ongoing debate in the senate but Optimate VS Populares partisanship bogged everything down to the point where the Italians felt they had no other options.

In the war itself Rome's greatest weapon was citizenship, its how they prevented certain tribes from joining the Italians and how they brought rebellious allies back in the fold. The Italians just wanted the full benefit of the empire they helped conquer.

Would they have gone full independent? If the romans had been unwilling to compromise quite probably. But It would have been an Italic state or a Roman one, Italy wasn't big enough for two states by that point. If the Italians had won they quite probably would have absorbed the empire as it was and used the same system of governance, just swapping out the romans at the top with Italians and the provinces probably wouldn't have noticed a difference. If the province's rebelled the Italians would have acted just like the romans would have, they would have considered that territory just as much theirs as the Roman Republic did.

Edit for typos

One of the main differences between the Romans and Italians during the Social War was their legal status. Romans were citizens of the Roman Republic and had certain legal rights and protections, while most Italians were not citizens and were subject to different laws and regulations. This disparity in legal status was one of the main grievances that sparked the Social War, as many Italians felt that they were being treated unfairly by the Roman Republic.

Another difference between the Romans and Italians during the Social War was their political power. Romans held most of the positions of power within the Roman Republic, including the consulship, the senate, and the military. By contrast, many Italians felt that they were being excluded from political power and were not given a say in important decisions that affected their lives.

In terms of culture and society, the Romans and Italians had many similarities, as both groups shared a common language, religion, and history.

Roman citizenship came with important civil rights.

Roman civilization since the Republic was legalistic and other tribes started to notice the advantages of it but trying to replicate it seems was not easy. So they wanted to the part of it.

Legalism could be rigid and excessive some times but it gives some predictability.