television news vs news show

television news and news show both are nouns.

Word	Noun	Adjective	Verb	Adverb
television news	Yes	No	No	No
news show	Yes	No	No	No

As nouns, news show is a hypernym of television news; that is, news show is a word with a broader meaning than television news:

television news: a television broadcast of news
news show: a program devoted to current events, often using interviews and commentary

Other hypernyms of television news include news, news program.

television news (noun)	news show (noun)
a television broadcast of news	a program devoted to current events, often using interviews and commentary