Comparisons of functions, their big-oh and their implications
As a counterexample you can take $f(n)=n$ and $g(n)=\sqrt{n}$. You can think that $f(n)=O(n^2)$ means that an upper bound for $f(n)$ is $n^2$ (of course, without considering multiplicative constant), so the fact that both $f$ and $g$ are bounded by $n^2$ does not implies nothing about the relative behavior of $f$ and $g$.