She would definitely consider herself a right wing candidate, and has even tried before the election to convince multiple right-wing parties to form an electoral alliance and run a single candidate (presumably either herself or the president of the National Liberal Party, the largest right wing party in Romania, Nicolae Ciucă).

This should not be confused to the far-right parties that backed her opponent for the second round, Călin Georgescu.

Basically Romania's political scene has one nominally left wing party, the Social Democratic Party (though their economic policies are often centrist, and their social policies are often right wing, with opposition to civil partnerships and even some resistance to abortion rights)*. They are quite hated as representatives of the pre-Revolution communist Romania, and as very corrupt. Their traditional electorate are those living in rural areas, those living in poverty, those working in the state apparatus, and generally with a lower education.

Then there is one traditional right-wing party, the National Liberal Party (liberal here in the "classical liberalism" sense, basically free market), that is slowly dying off, mostly due to the extremely unpopular current president who was elected on their lists; and due to governing in alliance with the SDP. They also have often been accused of corruption. They are relatively right wing both on economic and social issues.

Then, there is a much newer centre-right party, the Save Romania Union, which has similar economic policies to the NLP and is more socially liberal. They coasted to some success on a powerful anti-corruption, Change message, but have since become embroiled in internal infighting. There are also several small parties that split off from them that have very similar policies. For both these and the NLP, their traditional electorate is people living in larger cities, wealthier, especially white collar workers, with higher education.

All of the above parties are pro-EU, pro-NATO collaboration, agree on providing funds to Ukraine and so on.

Then there's the newest force, the hard right Alliance for the Union of Romanians (AUR, which also means "gold" in Romanian). They ran on populist somewhat left-wing promises (cheap houses for everyone!), hard right social conservatism (anti-LGBT, anti-abortion, very religious minded). There's also a splinter party with virtually the same promises, the SOS Romania Party, and a newer force, The Young People's party. All of these three are various degrees of euroskpetic, NATO skeptics and against providing resources to Ukraine.

Typically when someone in Romania says "the left", they mean the SDP; when they say "the right" they mean "the NLP and SRU", and when they want to refer to the other group, they'll either say "far right", "ultra nationalists", or their own preferred term "sovereignists" (from "national sovereignty").

* There is one small European-style left-wing party that ran in this election for the first time, but they only won 2,3% of the vote

The USR party is liberal right wing. They get accused of being "sexomarxisti" but that's mostly brainless chants.

They're pro free trade, freedoms, equality, all your runoff the mill liberal stuff.

Yeah, I would call that a centrist party. To me the "right" includes trampling on individual and social freedoms. But maybe I've been brainwashed by American politics.

Well, they are for privatizing health care I think? That's pretty right wing? But, yes your right wind is waaaaay more to the right than the norm.

Wouldn't that qualify a lot of the democratats as right wing since they are pro-censorship?

It is and they are. The slider of politics in the US is to the right and that was op's point.