How does a subset differ from a proper subset?

In set theory, the distinction between a subset and a proper subset lies in whether the two sets can be identical.

• Subset ($A\subseteq B$): A set $A$ is a subset of $B$ if every member of $A$ is also a member of $B$. Under this definition, a set is considered a subset of itself, meaning $A$ and $B$ can contain exactly the same elements.1
• Proper Subset ($A\subset B$): A proper subset is a subset that is not equal to the original set. In other words, $A$ is a proper subset of $B$ if every element of $A$ is in $B$, but there is at least one element in $B$ that is not in $A$.1

Essentially, while every proper subset is a subset, not every subset is a proper subset because the latter excludes the case where the two sets are equal.1