I’d say Serbs and Montenegrins are not “completely different people” or anything like that. The difference is more historical and regional.

A lot of Montenegrins come from old south Dinaric mountain world, where clan and tribal structures survived much longer than in most Serbian regions. These areas were hard to control properly so Ottoman rule didn't exist or it existed just on paper. Because of that, local tribes, brotherhoods, warrior traditions, blood feuds and clan identity etc. formed and stayed important for a very long time.

Ethnically and culturally, it was also not some pure isolated group. There were Slavic people, older Balkan populations, Vlachs, Albanians etc. But over time most of that became Slavic- speaking and Orthodox, especially in what became Montenegro.

So I would say Montenegrins and Serbs are very close, but Montenegrins developed in a more mountainous, tribal, clan-based environment. That made them a bit different in mentality and historical experience. More emphasis on tribe, honor, local autonomy, warrior identity, and mountain independence.

I think this is where the question gets complicated, because “Serb” can be used in more than one sense.

In a narrow modern national sense, Serbs and Montenegrins are two related but different identities. But historically and even today, many Montenegrins also saw themselves as Serbs. So someone can absolutely argue that Montenegrins are a regional branch of Serbs, especially if they are using “Serb” in that broader cultural-historical sense.

So my answer would be: they are extremely close, and depending on how you define the word “Serb,” Montenegrins can be seen either as a distinct but related people, or as a branch of the wider Serbian people.