Deities - Some of the earliest mermaids were goddesses who represented fertility, beauty, sex, but also a very destructive force of nature that can be found at sea. Most famous examples are Assyrian goddess Astarte, Greek Aphrodite, and African Mami Wata.
Mythical creatures - As the humans slowly learned how to survive in the sea, mermaids become part of the folklore and legends. They were no more gods, but spirits of the sea that brought both good and bad things to the sailors who encountered them.
Human transformation - Some myths speak of the mermaids that could transform into human state. Irish folklore mainly protects this lore to this day, and famous Persian book "Arabian Nights" speak on multiple occasions of the human race of sea dwellers (without fishtails) that can live both in water and on dry.
Commercialized modern day -Current pop-culture view of mermaids was formed in Hans Christian Andersen's fairytale "The Little Mermaid", and its modern day adaptation in Disney's animated movie of the same name.
Middle East -Babylonians and Assyrians were the first who showcased some of their gods as water creatures, most notably mermaid goddess Astarte.
Europe - European view of mermaids was greatly influenced by the Greek culture and their myths of Sirens - malevolent and carnivorous creatures that lured sailors to their deaths.
Asia - Chinese and Japanese cultures have their own stories about beautiful mermaids, who can grant riches and immortality to those who are worthy
Carribean - Haitian tradition of Vodou mentions water spirit called Lasiren, beautiful mermaid that bears close resemblance to the African goddess Mami Wata.
Africa - African goddess MamiWata had a big influence on the people of Africa, their diaspora and many other cultures around the world.
South America - The most famous siren from South America is Iara, Amazonian water spirit that is blamed for many deaths and misfortunes in that continent.
By their abilities
Mermaids - Lovely, wise and very shy creatures of the sea that in stories often fall in love with sailors and bear them children.
Sirens - Dangerous spirits of the sea that can conjure storm and fog, foretell death, read minds and wreak havoc of every level. For a long time, they were one of the sources of blame for many shipwrecks and deaths on long sea journeys.
ShipSavers - Sirens that are bound to help guide ships trough rough waters filled with dangerous rocks. Some scientist and historians claim that they represented nothing but migration patterns of manatees and dugongs, animals that were traditionally often mistaken for mermaids and sirens.
SpellSingers - Mermaids and Sirens who can lure the sailors to the sea, and the wandering isolated males to the shores where they are awaiting them. Sometimes with good intentions, sometimes not.
ShapeShifters - Several mermaid myths mention shape shifting sirens, which are able to transform into sea animals, fishes, snakes, and off course humans.
WeatherWorkers - Mermaids and Sirens who have ability to control the weather, usually at the expense of sailors who are nearby.
PearlWeepers - Popular myth of mermaids who can weep tears that instantly transforms into most beautiful pears. Some believe that they are made when mermaid walks on her newly form legs on the shore, which each new step being more painful than the last.