Nymphs are from Greek mythology. They’re minor female nature deities. Not really a goddess, they are more of a divine spirit or essence. The area they inhabit divines their classification. A water nymph could be anything from a naiad if she’s fresh water or a haliae if she’s of the sea or seashore (which would be closest to a mermaid). There are dozens of classifications as specific as wetlands, from springs, from rivers. The Greeks had a specific name for them all!
Nymphs and sprite are the easiest to confuse. However, sprite comes from the Latin spiritus to the French esprit to the English sprite. In Irish they are sometimes called spriggans; same thing. The confusing part: despite entomologically coming from the word spirit, they are not spirits. They are more fairies or elves. They are a fairy-like creature or ethereal entity. Not a minor nature deity like a nymph.
Mermaids have a woman’s upper body and a single fish’s tail for legs. Keyword: single. When you get down to the fish-part, a mermaid can become a lot of things that are not mermaid.
If she’s got seal fins for legs, not a mermaid. If she’s got a dolphin flipper, not a mermaid. It’s got to be a fish. By the way, when you add a serpent tail for legs, you get Melusine, a medieval monstrosity that was once a water sprite.
Mermaids can be male. That is okay. You’d just call him a merman.
Sirens are not mermaids at all. Only recently have they been depicted as having fish-like appendages. Originally, in Greek mythology, they were bird woman, with wings for arms and bird legs. Physically, their closest comparison would be the harpy.
Sirens live on rocky bluffs in the Mediterranean and earned a dangerous reputation for singing sailors into shipwrecking. Then they eat the remains. Mermaids are also of fickle nature, sometimes helping, sometimes drowning.
Also called a nixie, neck, nicor, or nokken. It’s a Germanic shapeshifting water spirit. Keyword: shapeshifting. They could be beguiling river maidens, white horses, wyverns. They’re all tied to water, though. A water spirit of a particular river might appear as a maiden whereas another might be a dragon. It depends on the spirit inhabiting the river.
Selkies are seal-folk from Celtic mythology and folklore. They aren’t part seal, like a woman with seal flippers. It’s a seal that can shed its skin and become a woman. The selkie is a fairy of sorts, a supernatural creature. It’s said on Midsummer’s Eve they shed their skins and dance on the seashores. If you steal their skin, they can’t transform back into their seal-form.
The rusalka is another spirit. It’s from Slavic mythology and folklore. However, it’s almost more of a literal spirit, as in ghost or demon. When a woman dies violently, drowns, or commits suicide near a water source, it’s said she’ll come back as a rusalka and haunt those water. They’re usually depicted as maidens in white shrouds walking the banks or shores. Not transforming, no creature parts. There most prevalent in the summer, for some reason.