The difference between Proof and Show

When used as nouns, proof means an effort, process, or operation designed to establish or discover a fact or truth, whereas show means a play, dance, or other entertainment.

When used as verbs, proof means to proofread, whereas show means to display, to have somebody see (something).

Proof is also adjective with the meaning: used in proving or testing.

check bellow for the other definitions of Proof and Show

Proof as a noun (countable):

An effort, process, or operation designed to establish or discover a fact or truth; an act of testing; a test; a trial.
Proof as a noun (uncountable):

The degree of evidence which convinces the mind of any truth or fact, and produces belief; a test by facts or arguments which induce, or tend to induce, certainty of the judgment; conclusive evidence; demonstration.
Proof as a noun:

The quality or state of having been proved or tried; firmness or hardness which resists impression, or does not yield to force; impenetrability of physical bodies.
Proof as a noun (obsolete):

Experience of something.
Proof as a noun (uncountable, obsolete):

Firmness of mind; stability not to be shaken.
Proof as a noun (countable, printing):

A proof sheet; a trial impression, as from type, taken for correction or examination.
Proof as a noun (countable, logic, mathematics):

A sequence of statements consisting of axioms, assumptions, statements already demonstrated in another proof, and statements that logically follow from previous statements in the sequence, and which concludes with a statement that is the object of the proof.
Proof as a noun (countable, mathematics):

A process for testing the accuracy of an operation performed. Compare prove, transitive verb, 5.
Proof as a noun (obsolete):

Armour of excellent or tried quality, and deemed impenetrable; properly, armour of proof.
Proof as a noun (US):

A measure of the alcohol content of liquor. Originally, in Britain, 100 proof was defined as 57.1% by volume (not used anymore). In the US, 100 proof means that the alcohol content is 50% of the total volume of the liquid, and thus, absolute alcohol would be 200 proof.

Proof as an adjective:

Used in proving or testing.

Examples:

"a proof load''; ''a proof charge"
Proof as an adjective:

Firm or successful in resisting.

Examples:

"proof against harm"

"waterproof''; ''bombproof''."
Proof as an adjective (of alcoholic liquors):

Being of a certain standard as to alcohol content.

Proof as a verb (transitive, intransitive, colloquial):

To proofread.
Proof as a verb (transitive):

To make resistant, especially to water.
Proof as a verb (transitive, cooking):

To allow yeast-containing dough to rise.
Proof as a verb (transitive, cooking):

To test the activeness of yeast.

Show as a verb (transitive):

To display, to have somebody see (something).

Examples:

"The car's dull finish showed years of neglect."

"All he had to show for four years of attendance at college was a framed piece of paper."
Show as a verb (transitive):

To bestow; to confer.

Examples:

"to show mercy; to show favour; lb dialectal show me the salt please"
Show as a verb (transitive):

To indicate (a fact) to be true; to demonstrate.
Show as a verb (transitive):

To guide or escort.

Examples:

"Could you please show him on his way. He has overstayed his welcome."

"They showed us in."
Show as a verb (intransitive):

To be visible; to be seen; to appear.

Examples:

"Your bald patch is starting to show."

"At length, his gloom showed."
Show as a verb (intransitive, informal):

To put in an appearance; show up.

Examples:

"We waited for an hour, but they never showed."
Show as a verb (intransitive, informal):

To have an enlarged belly and thus be recognizable as pregnant.
Show as a verb (intransitive, racing):

To finish third, especially of horses or dogs.

Examples:

"In the third race: Aces Up won, paying eight dollars; Blarney Stone placed, paying three dollars; and Cinnamon showed, paying five dollars."
Show as a verb (obsolete):

To have a certain appearance, such as well or ill, fit or unfit; to become or suit; to appear.

Show as a noun (countable):

A play, dance, or other entertainment.
Show as a noun (countable):

An exhibition of items.

Examples:

"art show; dog show'"
Show as a noun (countable):

A demonstration.

Examples:

"'show of force"
Show as a noun (countable):

A broadcast program/programme.

Examples:

"radio show; television show'"
Show as a noun (countable):

A movie.

Examples:

"Let's catch a show."
Show as a noun:

A project or presentation.

Examples:

"Let's get on with the show. Let's get this show on the road. They went on an international road show to sell the shares to investors. It was Apple's usual dog and pony show."
Show as a noun (uncountable):

Mere display or pomp with no substance. (Usually seen in the phrases "all show" and "for show".)

Examples:

"The dog sounds ferocious but it's all show."
Show as a noun:

Outward appearance; wileful or deceptive appearance.
Show as a noun (baseball, with "the"):

The major leagues.

Examples:

"He played AA ball for years, but never made it to the show."
Show as a noun (mining, obsolete):

A pale blue flame at the top of a candle flame, indicating the presence of firedamp.

Examples:

"rfquotek Raymond"
Show as a noun (archaic):

Pretence.
Show as a noun (archaic):

Sign, token, or indication.
Show as a noun (obsolete):

Semblance; likeness; appearance.
Show as a noun (obsolete):

Plausibility.
Show as a noun (medicine):

A discharge, from the vagina, of mucus streaked with blood, occurring a short time before labor.

The difference between Proof and Show

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