The classic definition of shanties is 19th century, Anglo-American, merchant marine, w/lyrics, &c &c.... So no pirates.

However, in recent, popular usage, the scope of its definition is sometimes expanded to admit a wider range of repertoire and characteristics, or to refer to a "maritime work song" in general. [wiki intro]

The difference is 2300 years of celeusmata & other clamour nauticus not labeled as songs but howls, cries, chants, shouts &c &c. No reason to think the local version of Howe hissa! (or whatever) wouldn't have been popular with the lads.