What is the difference between the statements

$$\exists K> 0\, \forall x \in \mathbb{R}\, : |f(x)|< K $$
and 
$$\forall x \in \mathbb{R}\, \exists K> 0\, : |f(x)|< K $$
I know what $\forall$ and $\exists$ mean but I just can't see a difference between the two statements? I know that say $f(x)=x^4$ has the first property I just don't really understand why. Any help would be gratefully appreciated.