art rock vs rock-and-roll

art rock and rock-and-roll both are nouns.

Word	Noun	Adjective	Verb	Adverb
art rock	Yes	No	No	No
rock-and-roll	Yes	No	No	No

As nouns, rock-and-roll is a hypernym of art rock; that is, rock-and-roll is a word with a broader meaning than art rock:

art rock: a style of rock music that emerged in the 1970s; associated with attempts to combine rock with jazz and other forms; intended for listening and not dancing
rock-and-roll: a genre of popular music originating in the 1950s; a blend of black rhythm-and-blues with white country-and-western

Other hypernyms of art rock include rock'n'roll, rock 'n' roll, rock, rock and roll, rock music.

art rock (noun)	rock-and-roll (noun)
a style of rock music that emerged in the 1970s; associated with attempts to combine rock with jazz and other forms; intended for listening and not dancing	a genre of popular music originating in the 1950s; a blend of black rhythm-and-blues with white country-and-western