What is the difference between closure property and commutative property?

Closure property says that if for any two natural or whole numbers a and b, $a\times b$ is also a natural or whole number then the set of natural or whole numbers is closed under $\times$ where $\times$ represents $+$, or $\times$.

For example,

Take two numbers 4 and 5, $4+5=9$ which is a natural (whole) number. Therefore, Natural(Whole) numbers are closed under addition.

The commutative property for addition or multiplication states that we can add or multiply natural or whole numbers in any order.

For example,

$2+3 = 3+2 = 5$

$2\times 3 = 3\times 2 = 6$