A differential form that gives rise to an orientation is of maximal degree and there aren't that many diffenrent differential forms of maximal degree. Consider a single point of the manifold and its tangent space. Let's assume it is of dimension $3$. Then there are several different one-forms, say $dx$ or $dy$. There are also several different two-forms, say $dx\wedge dy$ or $dy\wedge dz$. But there is only one three-form, namely $dx\wedge dy \wedge dz$, up to a real constant.
The same thing happens on the manifold. There is only one differential form of maximal degree at each point, up to a constant. But you can choose a different constant at each point. Hence if you have two different differential forms of maximum degree on a manifold they differ by a function.