When I click on "nepoate" it suggests both "nieces" and "granddaughters". Does it actually mean the same in romanian?
Yes, that is correct. It is also used for the daughter of a cousin (but I think that's also the case for “niece” in English).
I'm English and have never heard niece used for daughter of a cousin in English - the oxford English dictionary definition indicates only the daughter of a brother or sister or brother- or sister-in-law.