bridgehead vs beachhead

bridgehead and beachhead both are nouns.

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

As nouns, beachhead is a hyponym of bridgehead; that is, beachhead is a word with a more specific, narrower meaning than bridgehead:

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

Other hyponyms of bridgehead include airhead.

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