In a nutshell
Somewhere along the literary and mythological path, mermaids and sirens were confused into a creature: a creature that is half women and half fish and is known for its beautiful singing voice. Originally, only the mermaid was a half human, half fish-like creature, and a singing voice was not mentioned in early myths. Sirens were the singers, and they were actually half women, half birds.
Difference between mermaids and sirens
In today's world of pop culture, mermaid and sirens are often represented as the same figure. They are inevitably a beautiful woman from the waist down and a fish from the waist down, and they are known for their charming singing voices.
Originally, however, these two creatures were two completely separate myths.
Mermaids have been in myths and folklore since their first appearance in ancient Babylonian stories. Era, the fish god, was half human and half fish; after that it was the Greek god Triton. In fact, it was the Greeks who gave us the first descriptions of mermaids. Live specimens are said to have been studied by writers such as Pausanias in the second century, and described as having scales covering their entire bodies, gills, a fish-like mouth, and a scaly tail like that of a dolphin.
It was the Nereids of Greek mythology who produced the stories of the mermaids that were so popular in the mythology of the later seafarers. These sea nymphs received the features traditionally associated with the mermaid, half beautiful woman, half fish. These adorable creatures were known to mingle with people and give birth to children. The Greek hero Achilles was born of a mermaid, and some Greek families still claim mermaid blood in their lineage today. Nereids were found wherever there was water, including springs and wells. While mermaids have always been adorable, it was more their looks than their singing voice.
The sirens, known for their singing voices, were said to be of such beauty that sailors forgot what they were doing and simply stopped listening. Ships would crash on the rocks around Siren Island, killing those who fell victim to their song.
But the sirens were never half women and half fish. There were originally only three sirens, and they began as mortal human women who were the maidservants of Persephone, the daughter of the goddess Demeter. When Persephone was kidnapped by Hades, Demeter gave the three girls the bodies of birds to help them find the lost girl. When they could not find them, they finally gave up and moved to Anthemoessa Island, cursed by Demeter (who was angry that they had stopped searching) to stay in their half-bird form.
The sirens were further cursed when they took part in a singing competition with the Muses and lost the competition, their wings and many of their feathers.
Eventually the sirens died fulfilling a prophecy that someone should be able to resist their song. The sirens would perish. And they did it; When Odysseus had his men block their ears and then tied himself to the mast of his ship so that he could listen but not interfere, the sirens threw themselves into the sea and died as he passed.
Sirens and mermaids were confused for a long before Piers Anthony and CS Lewis assigned their singing voices to mermaids. Thomas Hoccleve's "La Male Regle" from the 1
Show me the evidence
Sea Monsters and Mermaids, Greek Myths and Legends by Adrienne Mayor
LiveScience: Mermaids & Mermen: Facts & Legends
TV tropes: sirens are mermaids