sum vs red ink

sum and red ink both are nouns.

Word	Noun	Adjective	Verb	Adverb
sum	Yes	No	Yes	No
red ink	Yes	No	No	No

As nouns, red ink is a hyponym of sum; that is, red ink is a word with a more specific, narrower meaning than sum:

sum (noun)	red ink (noun)
the whole amount	the amount by which the cost of a business exceeds its revenue
the choicest or most essential or most vital part of some idea or experience
a quantity obtained by the addition of a group of numbers
the final aggregate
a set containing all and only the members of two or more given sets
a quantity of money

sum (verb)	red ink (verb)
determine the sum of
be a summary of