The difference between Quire and Ream

Quire as a noun:

One-twentieth of a ream of paper; a collection of twenty-four or twenty-five sheets of paper of the same size and quality, unfolded or having a single fold.

Quire as a noun (bookbinding):

A set of leaves which are stitched together, originally a set of four pieces of paper (eight leaves, sixteen pages). This is most often a single signature (i.e. group of four), but may be several nested signatures.

Quire as a noun:

A book, poem, or pamphlet.

Quire as a verb (bookbinding):

To prepare quires by stitching together leaves of paper.

Quire as a noun (archaic):

A choir.

Quire as a noun:

One quarter of a cruciform church, or the architectural area of a church used by the choir, often near the apse.

Quire as a verb (intransitive):

To sing in concert.

Ream as a noun (UK, _, dialectal, Northern England, Scotland):

Cream; also, the creamlike froth on ale or other liquor; froth or foam in general.

Ream as a verb (UK, _, dialectal, Northern England, Scotland):

To cream; mantle; foam; froth.

Ream as a verb:

To enlarge a hole, especially using a reamer; to bore a hole wider.

Ream as a verb:

To shape or form, especially using a reamer.

Ream as a verb:

To remove (material) by reaming.

Ream as a verb:

To remove burrs and debris from a freshly bored hole.

Ream as a verb (slang):

To yell at or berate.

Ream as a verb (slang, vulgar):

To sexually penetrate in a rough and painful way, by analogy with definition 1.

Ream as a noun:

A bundle, package, or quantity of paper, nowadays usually containing 500 sheets.

Ream as a noun (chiefly, in the plural):

An abstract large amount of something.