A homophonic pun is where a word used in the pun sounds the same as another word with a different meaning. The two words don't have to sound the same, sometimes just sounding similar will be enough to make a pun.
Examples of Homophonic Puns
A police dog is often the scenter of a drug arrest.
This pun uses the similar sound of the words center and scenter to give this pun its two possible meanings, where a police dog may be the main reason a drug arrest is made i.e. the center of the arrest or where the police dog uses smell to determine someone possessing drugs i.e. the police dog is the 'scenter'.
Coins are mint to be.
In this pun, the word mint can be used interchangeably with the similarly sounding word meant. Mint is used with its meaning 'to make (coins, money, etc.) by stamping metal' and meant as the past tense of the verb 'to mean' with the definition 'to intend for a particular purpose, destination, etc.'.
Definitions and meanings sourced from Dictionary.com