Suppose that $M$ and $N$ are two atomic models of a complete theory $T$ in a countable language.
David Marker's Model Theory book:
Because the types in $S_n(T)$ realized in an atomic model are exactly the isolated types, M and N realize the same types.
I have this question that why the types in $S_n(T)$ realized in an atomic model are exactly the isolated types and if so why those models realize the same types?
If a complete type $p$ is realized by a $n$-tuple $\vec{a}$ in an atomic model, then $p$ is isolated by definition of atomic model.
If a type $p$ is isolated, say by formula $\varphi$, then since $T$ is complete $T\models\exists\vec{x}\varphi(\vec{x})$, so $p$ is realized in any model of $T$.
Finally, since $T$ is complete, $M\models\varphi$ is and only if $N\models\varphi$, which proves that they realize the same isolated types, and hence the same types by what we just proved.