In the book Computational Geometry, Algorithms and Applications from de Berg, van Kreveld, Overmars and schwarzkopf, I read the following in chapter 13.3 on Minkowski sums:
Sometimes $ P \oplus(-R(0,0))$ is referred to as the Minkowski difference of $P$ and $R(0,0)$. Since Minkowski differences are defined differently in the mathematics literature we shall avoid this.
Both $P$ and $R(0,0)$ are polygons, that is: a set of points in $\mathbb R^2$.
Beforehand, the following definitions are made:
For two sets $S_{1,2} \subset \mathbb R^2$, the Minkowski sum is defined as:
$$S_1 \oplus S_2 := \{p+q:p\in S_1, q \in S_2\}$$
For the vectors $p=(p_x,p_y)$ and $q=(q_x,q_y)$, the sum is defined as
$$p+q := (p_x+q_x,p_y+q_y)$$
For a point $p=(p_x,p_y)$, it's defined that
$$-p := (-p_x, -p_y)$$
and for a set $S$ it is defined that
$$-S := \{-p : p \in S\}$$
If not by $A \oplus -B$, how else is a Minkowski difference of the two sets defined? In what cases is that difference important?
