Wordplay

Word play or wordplay (also: play-on-words) is a literary technique and a form of wit in which the words that are used become the main subject of the work, primarily for the purpose of intended effect or amusement. Examples of word play include puns, phonetic mix-ups such as spoonerisms, obscure words and meanings, clever rhetorical excursions, oddly formed sentences, double entendres, and telling character names (such as in the play The Importance of Being Earnest, Ernest being a given name that sounds exactly like the adjective earnest).
Word play is quite common in oral cultures as a method of reinforcing meaning. Examples of text-based (orthographic) word play are found in languages with or without alphabet-based scripts; for example, see homophonic puns in Mandarin Chinese.
Pun

The pun, also called paronomasia, is a form of word play that exploits multiple meanings of a term, or of similar-sounding words, for an intended humorous or rhetorical effect. These ambiguities can arise from the intentional use of homophonic, homographic, metonymic, or figurative language. A pun differs from a malapropism in that a malapropism is an incorrect variation on a correct expression, while a pun involves expressions with multiple correct interpretations. Puns may be regarded as in-jokes or idiomatic constructions, as their usage and meaning are specific to a particular language and its culture.
Puns have a long history in human writing. Sumerian cuneiform and Egyptian hieroglyphs were originally based on punning systems, and the Roman playwright Plautus was famous for his puns and word games. Punning has been credited as the fundamental concept behind alphabets, writing, and even human civilization.

Wikipedia

Wordplay (noun)
A humorous play on words; such plays on words collectively.
Wordplay (noun)
A witty verbal exchange; such exchanges collectively.

Pun (verb)
To beat; strike with force; to ram; to pound, as in a powder, to pulverize.
Pun (verb)
To make or tell a pun; to make a play on words.
"We punned about the topic until all around us groaned."
Pun (noun)
A joke or type of wordplay in which similar senses or sounds of two words or phrases, or different senses of the same word, are deliberately confused.
"The pun is the lowest form of wit."
Pun (noun)
: a unit of length equivalent to about 0.3{{nbsp}}cm.

Wiktionary

Wordplay (noun)
A more or less subtle playing upon the meaning of words.

Pun
To pound.
Pun
To persuade or affect by a pun.
Pun (noun)
A play on words which have the same sound but different meanings; an expression in which two different applications of a word present an odd or ludicrous idea; a kind of quibble or equivocation.
Pun (verb)
To make puns, or a pun; to use a word in a double sense, especially when the contrast of ideas is ludicrous; to play upon words; to quibble.

Webster Dictionary

Wordplay (noun)
a humorous play on words;
"I do it for the pun of it"
"his constant punning irritated her"

Pun (noun)
a humorous play on words;
"I do it for the pun of it"
"his constant punning irritated her"
Pun (verb)
make a play on words;
"Japanese like to pun--their language is well suited to punning"

Princeton's WordNet