normal and mean both are nouns.

normal and mean both are adjectives.

normal is not a verb while mean is a verb.

normal (noun)	mean (noun)
something regarded as a normative example	an average of n numbers computed by adding some function of the numbers and dividing by some function of n

normal (adjective)	mean (adjective)
conforming with or constituting a norm or standard or level or type or social norm; not abnormal	approximating the statistical norm or average or expected value
in accordance with scientific laws	characterized by malice
being approximately average or within certain limits in e.g. intelligence and development	having or showing an ignoble lack of honor or morality
forming a right angle	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

normal (verb)	mean (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