fall vs season

fall and season both are nouns.

Word	Noun	Adjective	Verb	Adverb
fall	Yes	No	Yes	No
season	Yes	No	Yes	No

As nouns, season is a hypernym of fall; that is, season is a word with a broader meaning than fall:

fall: the season when the leaves fall from the trees
season: one of the natural periods into which the year is divided by the equinoxes and solstices or atmospheric conditions

Other hypernyms of fall include time of year.

fall (noun)	season (noun)
a sudden drop from an upright position	one of the natural periods into which the year is divided by the equinoxes and solstices or atmospheric conditions
the act of surrendering (usually under agreed conditions)	a recurrent time marked by major holidays
a lapse into sin; a loss of innocence or of chastity	a period of the year marked by special events or activities in some field
a sudden sharp decrease in some quantity
a free and rapid descent by the force of gravity
a sudden decline in strength or number or importance
when a wrestler's shoulders are forced to the mat
a movement downward
a downward slope or bend
the season when the leaves fall from the trees
the time of day immediately following sunset

fall (verb)	season (verb)
occur at a specified time or place	make healthy
decrease in size, extent, or range	make more temperate, acceptable, or suitable by adding something else
pass suddenly and passively into a state of body or mind	lend flavor to
be born, used chiefly of lambs
come out; issue
assume a disappointed or sad expression
begin vigorously
come as if by falling
be cast down
go as if by falling
fall or flow in a certain way
move downward and lower, but not necessarily all the way
move in a specified direction
descend in free fall under the influence of gravity
slope downward
drop oneself to a lower or less erect position
lose an upright position suddenly
to be given by assignment or distribution
be captured
fall to somebody by assignment or lot; passed
come into the possession of
to be given by right or inheritance
be inherited by
lose office or power
yield to temptation or sin
suffer defeat, failure, or ruin
lose one's chastity
die, as in battle or in a hunt
be due
come under, be classified or included
touch or seem as if touching visually or audibly
fall from clouds