palmistry vs fortune telling

palmistry and fortune telling both are nouns.

Word	Noun	Adjective	Verb	Adverb
palmistry	Yes	No	No	No
fortune telling	Yes	No	No	No

As nouns, fortune telling is a hypernym of palmistry; that is, fortune telling is a word with a broader meaning than palmistry:

palmistry: telling fortunes by lines on the palm of the hand
fortune telling: the art or gift of prophecy (or the pretense of prophecy) by supernatural means

Other hypernyms of palmistry include divination, foretelling, soothsaying.

palmistry (noun)	fortune telling (noun)
telling fortunes by lines on the palm of the hand	the art or gift of prophecy (or the pretense of prophecy) by supernatural means