three kinds of pun

There are three kinds of people. Those that can count and those that can't.
And there are three kinds of pun.
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Homographic (antanaclasis): The use of multiple meanings from a single spelling. For example, 'pickle' could be something you eat, or a nasty situation.

Homophonic (polyptoton): The use of similar sounds with different spellings. For example, 'idle' and 'idol'

Double-sound: As used in the typical "knock-knock" joke, when you substitute one sound for another. Knock knock.
"Who's there?"
"Orange."
"Orange who?"
"Orange you going to open the door?"