gesture vs sign

gesture and sign both are nouns.

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

As nouns, sign is a hyponym of gesture; that is, sign is a word with a more specific, narrower meaning than gesture:

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

As verbs, sign is a hyponym of gesture; that is, sign is a word with a more specific, narrower meaning than gesture:

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

gesture (noun)	sign (noun)
motion of hands or body to emphasize or help to express a thought or feeling	structure displaying a board on which advertisements can be posted
something done as an indication of intention	a public display of a message
the use of movements (especially of the hands) to communicate familiar or prearranged signals	a gesture that is part of a sign language
	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

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

gesture (verb)	sign (verb)
show, express or direct through movement	be engaged by a written agreement
	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