add vs sum up

add and sum up both are verbs.

Word	Noun	Adjective	Verb	Adverb
add	No	No	Yes	No
sum up	No	No	Yes	No

As verbs, add and sum up are synonyms defined as:

Other synonyms of add include add together, add up, sum, summate, tally, tot, tot up, total, tote up.

add (verb)	sum up (verb)
make an addition (to); join or combine or unite with others; increase the quality, quantity, size or scope of	give a summary (of)
make an addition by combining numbers	determine the sum of
determine the sum of	be a summary of
state or say further
bestow a quality on
constitute an addition