Both versions are called sirens, Rome took a lot of their mythology from Greece, but something got lost in translation along the way, and bird women turned into fish women.

Both are still technically correct mythological references, the Greek siren came first, but that doesn't make the Roman Siren less valid. Typically in modern culture, people think of sirens as being mermaid-like, and so with pop culture things like children's cartoons, they're going to use the Roman version, because that's what people think of as being a "siren". For mythology nerds, it's a bit annoying, but misleading it's probably not the right term, because both are valid myths, depending on what culture you're looking at.