mean vs first moment

mean and first moment both are nouns.

As nouns, first moment is a hyponym of mean; that is, first moment is a word with a more specific, narrower meaning than mean:

mean: an average of n numbers computed by adding some function of the numbers and dividing by some function of n
first moment: the sum of the values of a random variable divided by the number of values

Other hyponyms of mean include expectation, expected value, arithmetic mean, geometric mean, harmonic mean, Winsorized mean, weighted arithmetic mean, weighted average, weighted mean.

mean (noun)	first moment (noun)
an average of n numbers computed by adding some function of the numbers and dividing by some function of n	the sum of the values of a random variable divided by the number of values

mean (adjective)	first moment (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)	first moment (verb)
mean or intend to express or convey
have as a logical consequence
denote or connote
have in mind as a purpose
have a specified degree of importance
intend to refer to
destine or designate for a certain purpose