There were all kinds of strange creatures living in this world, and there were several kinds of them that could charm people with songs.
As it happened, both mermaids and sirens had this ability and they all lived in the sea. Therefore, people who had a scanty knowledge of the facts compared the two, or even confused the two.
In this matter, the sirens certainly had no objection. What they cared about was eating people. As for what people thought; well, when you ate bread, did you care about what bread thought?
But mermaids had objections; big ones!
"Eat meat?! This is a smear to us!"
Well, what they really cared about was of whether or not they ate people, but the dignity of being a vegetarian.