On page 27 of Foundations of Mathematics (Stewart & Tall, 2015) they derive the expression
$-1/10^n < x - y < 1/10^n$
and go on to state that "if two real numbers have the same decimal expansion to $n$ places, then they differ by at most $1/10^n$.
I am interpreting this to mean that there exist at least two real numbers with the same decimal expansion to $n$ places such that their difference is equal to $1/10^n$. But this does not make sense to me since such a pair of real numbers would then not have the same decimal expansion to $n$ places. To my mind, the difference between the two numbers should be $less$ than $1/10^n$. How do I resolve this apparent contradiction?
There is no contradiction. The text claims that for all $x,y$ with the given condition on their decimal expansions, we have $|x-y|\le 10^{-n}$. You interprete this as implying that for some such $x,y$ we have $|x-y|=10^{-n}$, and that is unjustified.
Note that there is no number $a$ smaller than $10^{-n}$ such that we colud say that $|x-y|\le a$.
Also not that not everybody considers decimal expansion unique, or normalozed to not end in infinitely many nines. So for example $x=0.1230000\ldots$ and $y=0.1239999\ldots$ differ by exactly $10^{-3}$. Then again, the authors seem to not allow such corner cases as they explicitly derive $-1/10^n<x-y<1/10^n$, i.e., indeed the stronger claim that the difference is strictly less than $10^{-n}$. Nobody can forbid them to weaken their claim.