the concept of a pun is usually used in one context, and one context alone, and that is to refer to a particular type of joke, in which the person says one word which has two different meanings, and provides an opportunity to make ourselves aware of both of the meanings of this word in the same instance. See: puns (humor style) for more examples of this thing. However, I have come up with the idea or come to the conclusion that this concept of creating an opportunity to become aware of two different or separate meanings that exist within the space of the same title might be important or valuable for accessing information which is conceptually related to this, but has none of the connotations for example that it is a stupid joke that a dad made. Afterwards it may be important and/or possible to reconcile these contradictory connotations in the sense that we may become able to import some of them and apply it to the other.
So, in essence, the subject at hand is "two things with the same title but different meanings."