sign vs gesture

sign and gesture both are nouns.

Word	Noun	Adjective	Verb	Adverb
sign	Yes	Yes	Yes	No
gesture	Yes	No	Yes	No

As nouns, gesture is a hypernym of sign; that is, gesture is a word with a broader meaning than sign:

sign: a gesture that is part of a sign language
gesture: the use of movements (especially of the hands) to communicate familiar or prearranged signals

Other hypernyms of sign include motion.

As verbs, gesture is a hypernym of sign; that is, gesture is a word with a broader meaning than sign:

sign: make the sign of the cross over someone in order to call on God for protection; consecrate
gesture: show, express or direct through movement

Other hypernyms of sign include gesticulate, motion.

sign (noun)	gesture (noun)
structure displaying a board on which advertisements can be posted	motion of hands or body to emphasize or help to express a thought or feeling
a public display of a message	something done as an indication of intention
a gesture that is part of a sign language	the use of movements (especially of the hands) to communicate familiar or prearranged signals
any nonverbal action or gesture that encodes a message
a character indicating a relation between quantities
a perceptible indication of something not immediately apparent (as a visible clue that something has happened)
a fundamental linguistic unit linking a signifier to that which is signified
an event that is experienced as indicating important things to come
(astrology) one of 12 equal areas into which the zodiac is divided
having an indicated pole (as the distinction between positive and negative electric charges)
(medicine) any objective evidence of the presence of a disorder or disease

sign (adjective)	gesture (adjective)
used of the language of the deaf

sign (verb)	gesture (verb)
be engaged by a written agreement	show, express or direct through movement
communicate silently and non-verbally by signals or signs
mark with one's signature; write one's name (on)
make the sign of the cross over someone in order to call on God for protection; consecrate
communicate in sign language
place signs, as along a road
approve and express assent, responsibility, or obligation
engage by written agreement