mean vs stand for

mean is a noun but stand for is not a noun.

As verbs, stand for is a hyponym of mean; that is, stand for is a word with a more specific, narrower meaning than mean:

Other hyponyms of mean include represent, typify, symbolise, symbolize, signify, import, spell, aim, get, aim, drive.

As verbs, mean and stand for are synonyms defined as:

Other synonyms of mean include intend, signify.

mean (noun)	stand for (noun)
an average of n numbers computed by adding some function of the numbers and dividing by some function of n

mean (adjective)	stand for (adjective)
approximating the statistical norm or average or expected value
characterized by malice
having or showing an ignoble lack of honor or morality
marked by poverty befitting a beggar
(used of persons or behavior) characterized by or indicative of lack of generosity
(used of sums of money) so small in amount as to deserve contempt
of no value or worth
very good; of the highest quality

mean (verb)	stand for (verb)
mean or intend to express or convey	express indirectly by an image, form, or model; be a symbol
have as a logical consequence	denote or connote
denote or connote	take the place of or be parallel or equivalent to
have in mind as a purpose	tolerate or bear
have a specified degree of importance
intend to refer to
destine or designate for a certain purpose