Sea shanties are a form of maritime work song that cannot have instrumental accompaniment. "Sea song" is a broader term for other forms of maritime music, such as songs that have instrumental backing. Many of the things popularly referred to as "sea shanties" are really sea songs.

JSTOR

Wikipedia

Sea Shanty Facts, History and Meanings (rmg.co.uk)

What is a "sea shanty"? - Many Musics of America (amsmusicology.org)

For some reason, Wikipedia decided to have "sea song" be a section of the "sea shanty" page even though it acknowledges the distinction.