The phrases "has ... in " vs. "contains ... of" in Baby Rudin

Question

Consider the following two statements. (Assume $E \subseteq K$.)

$E$ has a limit point in $K$.

vs.

$E$ contains a limit point of $K$.

What do they each mean and how are they different?

Answer 1

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 $E$.

Answer 2

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 $y\in E$.