The difference between Smart and Witty

When used as adjectives, smart means exhibiting social ability or cleverness, whereas witty means wise, having good judgement.

Smart is also noun with the meaning: a sharp, quick, lively pain.

Smart is also verb with the meaning: to hurt or sting.

check bellow for the other definitions of Smart and Witty

Smart as a verb (intransitive):

To hurt or sting.

Examples:

"After being hit with a pitch, the batter exclaimed "Ouch, my arm smarts!"
Smart as a verb (transitive):

To cause a smart or sting in.
Smart as a verb (intransitive):

To feel a pungent pain of mind; to feel sharp pain or grief; to suffer; to feel the sting of evil.

Smart as an adjective:

Exhibiting social ability or cleverness.
Smart as an adjective (informal):

Exhibiting intellectual knowledge, such as that found in books.
Smart as an adjective (often, in combination):

Equipped with digital/computer technology.

Examples:

"smart bomb'', ''smart car"

"smartcard'', ''smartphone"
Smart as an adjective:

Good-looking.

Examples:

"a smart outfit"
Smart as an adjective:

Cleverly shrewd and humorous in a way that may be rude and disrespectful.

Examples:

"He became tired of his daughter's sarcasm and smart remarks''."

"Don't get smart with me!"
Smart as an adjective:

Sudden and intense.
Smart as an adjective:

Causing sharp pain; stinging.
Smart as an adjective:

Sharp; keen; poignant.

Examples:

"a smart pain"
Smart as an adjective (US, Southern, dated):

Intense in feeling; painful. Used usually with the adverb intensifier right.

Examples:

"He raised his voice, and it hurt her feelings right smart."

"That cast on his leg chaffs him right smart."
Smart as an adjective (archaic):

Efficient; vigorous; brilliant.
Smart as an adjective (archaic):

Pretentious; showy; spruce.

Examples:

"a smart gown"
Smart as an adjective (archaic):

Brisk; fresh.

Examples:

"a smart breeze"

Smart as a noun:

A sharp, quick, lively pain; a sting.
Smart as a noun:

Mental pain or suffering; grief; affliction.
Smart as a noun:

Smart-money.
Smart as a noun (slang, dated):

A dandy; one who is smart in dress; one who is brisk, vivacious, or clever.

Witty as an adjective (obsolete):

Wise, having good judgement.
Witty as an adjective (archaic):

Possessing a strong intellect or intellectual capacity; intelligent, skilful, ingenious.
Witty as an adjective:

Clever; amusingly ingenious.

Examples:

"His speech was both witty and informative."
Witty as an adjective:

Full of wit.

Examples:

"His frequent [[quip]]s mark him as particularly witty."
Witty as an adjective:

Quick of mind; insightful; in possession of wits.

Examples:

"She may have grown older, but she has grown no less witty."