Barbary pirate vs sea robber

Barbary pirate and sea robber both are nouns.

Word	Noun	Adjective	Verb	Adverb
Barbary pirate	Yes	No	No	No
sea robber	Yes	No	No	No

As nouns, sea robber is a hypernym of Barbary pirate; that is, sea robber is a word with a broader meaning than Barbary pirate:

Barbary pirate: a pirate along the Barbary Coast
sea robber: someone who robs at sea or plunders the land from the sea without having a commission from any sovereign nation

Other hypernyms of Barbary pirate include buccaneer, pirate, sea rover.

Barbary pirate (noun)	sea robber (noun)
a pirate along the Barbary Coast	someone who robs at sea or plunders the land from the sea without having a commission from any sovereign nation