Is there a difference between $\sin^2(x)$ and $\sin(x)^2$? Is there a difference between these? Or are they the same?
If they're the same, then why does $\sin^2(x)$ seem like its used more often?

No difference,
$\sin^2(x) = \sin(x)^2 = (\sin(x))^2$
$\sin^2(x)$ is used more often because it's easier to write especially dealing with complex equations.
