beachhead vs bridgehead

beachhead and bridgehead both are nouns.

Word	Noun	Adjective	Verb	Adverb
beachhead	Yes	No	No	No
bridgehead	Yes	No	No	No

As nouns, bridgehead is a hypernym of beachhead; that is, bridgehead is a word with a broader meaning than beachhead:

beachhead: a bridgehead on the enemy's shoreline seized by an amphibious operation
bridgehead: an area in hostile territory that has been captured and is held awaiting further troops and supplies

Other hypernyms of beachhead include foothold.

beachhead (noun)	bridgehead (noun)
an initial accomplishment that opens the way for further developments	an area in hostile territory that has been captured and is held awaiting further troops and supplies
a bridgehead on the enemy's shoreline seized by an amphibious operation	a defensive post at the end of a bridge nearest to the enemy