Consider the following two statements. (Assume $E \subseteq K$.)
$E$ has a limit point in $K$.
$E$ contains a limit point of $K$.
What do they each mean and how are they different?
The first says that there exists an $x\in K$ such that $x$ is a limit point of $E$, whereas the second says that there is a limit point $x$ of $K$ that lies within $E$.
The first one means that there is a limit point of $E$, say $x$, where $x\in K$.
The second one means that there is a limit point of $K$, say $y$, where $y\in E$.