It’s the type that has gills on the neck, similar to how fish have gills behind their heads.
In my view, it likely breathes underwater through the gills on its neck, and breathes through its lungs when out of the water.
The lungs also function like a swim bladder, giving it buoyancy.
This type can live not only around islands in the sea, but also in freshwater environments.

Sometimes, in certain unofficial works, merfolk with neck gills are depicted as being unable to breathe outside the water.
Personally, I wonder whether they should be able to breathe with the lungs in their chest, and I question whether such depictions are a setting inconsistency.
However, I can still accept these portrayals, since I see them as attempts to explore detailed world-building choices.

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