stock market index vs stock index

stock market index and stock index both are nouns.

Word	Noun	Adjective	Verb	Adverb
stock market index	Yes	No	No	No
stock index	Yes	No	No	No

As nouns, stock market index and stock index are synonyms defined as:

stock market index and stock index: index based on a statistical compilation of the share prices of a number of representative stocks

stock market index (noun)	stock index (noun)
index based on a statistical compilation of the share prices of a number of representative stocks	index based on a statistical compilation of the share prices of a number of representative stocks