On the page of Widipeida about Ito Lemma (https://en.wikipedia.org/wiki/It%C3%B4%27s_lemma) the formula is
$df = \frac{\partial f}{\partial t}dt + \frac{\partial f}{\partial x}dx + \frac{1}{2}\frac{\partial^2 f}{\partial x^2}dx^2 + \cdots $
where the coefficient before $\frac{\partial^2 f}{\partial x^2}dx^2$ is $\frac{1}{2}$
But on the page of Wikipedia about Geometri Brownian Motion(https://en.wikipedia.org/wiki/Geometric_Brownian_motion), I found a formula which is $d(\ln{St}) = \frac{dSt}{St} - \frac{1}{2}\frac{1}{St^2}dSt^2$
The coefficent before $\frac{1}{St^2}dSt^2$ is -$\frac{1}{2}$
Could you please explain why in the first formula is 1/2 but in the second is -1/2?
Thanks!