stock index vs stock market index

stock index and stock market index both are nouns.

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

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

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

stock index (noun)	stock market 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