Your confusion is warranted. There are three competing theories, and there is no scholarly consensus which one is "the real truth". More precisely this was (is) a highly politicised question in the XXth century, and the division of opinion among scholars highly correlates with one's ethnicity.

The first theory is that of the Daco-Roman continuity. This states that Romanians are direct descendants of the Roman colonists of Provincia Dacia and the Dacians themselves. According to this theory, after Aurelian's decision to evacuate the province, a sizeable portion of the population stayed behind, were forced to live in the mountains by subsequent conquerors, and here they weathered the turbulent history of the region, and then (re-)colonised the territories that comprise Romania currently.

The second one, the immigration-theory is that Romanians are chiefly descendant of the Latin speaking population of the Balkan provinces like Illyricum, Dalmatia or Moesia. With the fall of the Western Roman Empire, and the shrinking of the Eastern Roman Empire these people were forced into the mountains of the Balkans by subsequent conquerors, where they weathered the turbulent history of the region, and then (re-)colonised the territories that comprise Romania currently.

The third theory, the admigration theory is, that Latin speaking people for the last 2000 years lived more or less continuously in territories that comprise Romania currently, but these Latin-speaking populations were constantly reinforced by the immigrants from other former Roman provinces, like Illyria and Dalmatia.

As you can see, there is no real argument whether or not Romanian is a Latin language, that much is beyond dispute. The contentious issue is where exactly the ethnogenesis of the Romanian people happened.