BadPuns.com features a section called Dotty Definitions. This section contains short puns based on the concept of a dictionary definition - a word is presented, followed by a definition. Except in this case, the definitions are wordplays, and not the actually definition of the word.
Although this sounds like a fairly tight category, there is in fact considerable variation on the theme, and there are at least three distinct sub-categories of this type of joke, though here they are kept all within the same section.
The three categories are Daffynitions, Fictionary, and of course Dotty Definitions themselves.
To distinguish between them:
In Daffynitions, the wordplay is in the definition. An ordinary word is given, but the definition given is a wordplay on it. An good example is "Benign: What you'll be after you be eight."
In Fictionary, the word given is a made-up one, usually created by combining syllables from other words. The name Fictionary is itself an example of this.
The remaining category, called Dotty Definitions here for want of a better name, gives an accurate, but warped definition of a word. My favourite is this one: "Cold War: A state of suspended ammunition".
On BadPuns.com, all three types are lumped together in a single category.