add vs alter

add and alter both are verbs.

Word	Noun	Adjective	Verb	Adverb
add	No	No	Yes	No
alter	No	No	Yes	No

As verbs, alter is a hypernym of add; that is, alter is a word with a broader meaning than add:

Other hypernyms of add include change, modify.

add (verb)	alter (verb)
make an addition (to); join or combine or unite with others; increase the quality, quantity, size or scope of	remove the ovaries of
make an addition by combining numbers	become different in some particular way, without permanently losing one's or its former characteristics or essence
determine the sum of	cause to change; make different; cause a transformation
state or say further	insert words into texts, often falsifying it thereby
bestow a quality on	make an alteration to
constitute an addition