Romania is part of the Balkans. That alone should tell you that the country’s ethnicity has been contested for quite a while…maybe 2000 years or so…
For instance, I know there is a debate on whether the Romanians are directly descended from the Daco-Romanians indigenous to the area which they now inhabit (once called Dacia, then Wallachia), or whether they are mainly descendants of migrating Balkan tribes known as Vlachs or Wallachs. Much of this debate concerns disputes between Hungarians and Romanians over territories such as Transylvannia, Banat and so on.
What’s remarkable is that Dacia was only a Roman province from around 117 AD to the early 4th century - yet it became Romance speaking, while many areas in Europe that were Latin spaking Roman for far longer no longer have a Latin based language. Part of this may have been due to the fact that the Dacians who lived in the area adopted Roman culture rapidly, and a fair number of Roman soldiers arrived to fortify the natural borders along the Carpathian mountains. But some pople feel that this is not suficient to explain how Romania is so “Romanized”. They are inclined to believe that much of the Romanian population streamed in as refugees from the general mayhem of East Central Europe after the fall of the Roman Empire.
I believe to this day some people who aren’t to big on the Romanians and their claims to Roman heritage refer to Romanians as “Vlachs” and not as Romanians. But most people limit the term “Vlach” (or “Aromanian”) to various once nomadic groups of Romance speakers found in Albania, Northern Greece, Bulgaria, and former Yugoslavia. However, they are the closest linguistic relatives of the Romanians, which suggests a more migratory origin of the Romanians. (Romanians for their part insist that the Vlachs may be refugees from later invasions of Romania by Magyars, Turks and so on).
Their language is a Romance language - descended from Latin. In fact, if you can read Italian you can half work it out. EG: They pronounce their word for water “apuh” - compare with “acqua”.
So they are fully entitled to see themselves as culturally descended from Rome and different from Slavs or Magyars, by whom they are surrounded.
To look at, many of them also have Italian/Latin features, including what is sometimes described as an “olive” tint to their skin.