fan palm vs palm tree

fan palm and palm tree both are nouns.

Word	Noun	Adjective	Verb	Adverb
fan palm	Yes	No	No	No
palm tree	Yes	No	No	No

As nouns, palm tree is a hypernym of fan palm; that is, palm tree is a word with a broader meaning than fan palm:

fan palm: palm having palmate or fan-shaped leaves
palm tree: any plant of the family Palmae having an unbranched trunk crowned by large pinnate or palmate leaves

Other hypernyms of fan palm include palm.

fan palm (noun)	palm tree (noun)
palm having palmate or fan-shaped leaves	any plant of the family Palmae having an unbranched trunk crowned by large pinnate or palmate leaves