  We compare the sets of homotopy classes of gradient and proper gradient
vector fields in the plane. Namely, we show that gradient and proper gradient
homotopy classifications are essentially different. We provide a complete
description of the sets of homotopy classes of gradient maps from
$\mathbb{R}^n$ to $\mathbb{R}^n$ and proper gradient maps from $\mathbb{R}^2$
to $\mathbb{R}^2$ with the Brouwer degree greater or equal to zero.
