Both "Chipped Beef" and "A Plague of Tics" deal with the idea of irrepressible identity -- or the ways that personality informs identity despite circumstance and despite social atmosphere.
In "Chipped Beef" the narrator begins the story with a version of his family life that adheres to an ideal vision of family that springs from his personality. As an anal, orderly, pompous and dreamy type of person, the narrator prefers a vision of life in an admirable and wealthy family to his actual life with a mother who denigrates his sense of superiority and an ever-growing number of sisters.
Importantly, the narrator's preferences are not produced by his environment. Rather, they run contrary to his environment.
It wasn't that we were poor. According to my parents, we were far from it, just not far enough from it to meet my needs. I wanted a home with a moat rather than a fence. In order to get a decent night's sleep, I needed an airport named in our honor.
His mother calls him a snob and the narrator does not attempt to deny her claim. She also suggests a distance between the narrator's ideals and her own system of values and perspectives. The narrator is the creator of his own predilections. His identity as part of his family is at odds with his personality, which insists on pomp and strict order.
"A Plague of Tics" also explores the idea that the narrator's personality is not the product of his upbringing and instead comes from his own internal life -- an internal life that his mother and father neither find explicable or charming (though his mother patiently incorporates his many tics and foibles into her sense of normalcy).
The narrator's mother tells his teachers that she does not know where he gets his tics from. The narrator also does not seem to want to probe the origins of his need to rock on his bed, lick doorknobs and roll his eyes deep into his eye sockets.
Again, his identity as part of a family or part of a class of students stands as a separate source than his own personality, which drives his behavior to a point of neurotic oppression. He cannot escape or suppress his personality and this internal force compels him to act against social principles of normalcy and decorum.
Taken one step further, the internal force that produces the narrator's tics is also somehow set apart from his deepest sense of self. His sensitivity to the urges to lick things and rock back and forth is only one part of a larger consciousness of self. He experiences the quirks of his personality from a standpoint that shows him to be aware of social norms (to some degree) but also aware of a basic inner being that is soothed by acting on those quirks and, ultimately, soothed and calmed by smoking cigarettes.
Other themes explored in these stories include familial relationships and the recognition of the suffering/plight of loved ones.