short account vs index number

short account and index number both are nouns.

Word	Noun	Adjective	Verb	Adverb
short account	Yes	No	No	No
index number	Yes	No	No	No

As nouns, index number is a hypernym of short account; that is, index number is a word with a broader meaning than short account:

short account: the aggregate of short sales on an open market
index number: a number or ratio (a value on a scale of measurement) derived from a series of observed facts; can reveal relative changes as a function of time

Other hypernyms of short account include index, indicant, indicator.

short account (noun)	index number (noun)
the aggregate of short sales on an open market	a number or ratio (a value on a scale of measurement) derived from a series of observed facts; can reveal relative changes as a function of time
a brokerage account of someone who sells short (sells securities he does not own)