We can see some similarities if we look at the relationships which focus each of these stories.

Each story features a pseudo-love affair or presents a protagonist with a love interest where his interest is willful and desperate but not ultimately romantic. In Catcher in the Rye the love interest is the younger sister and in Rushmore it is the older teacher.

In each case the love interest can be said to represent the comment or judgment that is central to the yearnings (and failures) of the protagonist. For Caulfield the world is not innocent as he would like it to be, as his sister is. In Rushmore the older teacher represents the sophistication that the protagonist finds lacking in his world.

On a more surface-oriented level, we can connect these stories by looking at the actions of the protagonists which are abnormal for a person of this age, more than a little wild, and driven by a need to be different (or, driven by an unwillingness to accept himself as he is).

Each story also explores themes of isolation, resentment, existential striving, and displacement. To rephrase a point from above as a theme, we can say that love, in both Rushmore and Catcher in the Rye, is a mode or method of identification where the protagonist sees himself as being like the loved one.