What is the difference between mutually exclusive and independent events?

If the events are $A$ and $B$, then:
$A$ and $B$ are Mutually exclusive $\iff P \left(A \cap B\right) = 0$
$A$ and $B$ are Independent $\iff P \left(A \cap B\right) = P \left(A\right) \cdot P \left(B\right)$