The dex defines a "fluviu" as a big river that ends in either a sea or an ocean. The Romanian wikipedia page for it pretty much agrees and has "Main stem" as its corresponding English article (a term I've never heard of)
Duolingo gives no information regarding the geography of said river so either term should be accepted if it is used correcting in the sentence. Unless we are supplied with a visual of the river in question!
So the "Dunărea" than should be a fluviu, shouldn't it? And the "Timiș"ore the "Mureș" is a râu. But what's a little river, like in the mountains for example the "Caraș"? Is it also a râu, if it's so small, that you can cross it without a bridge?