Difference in definitions of “Minkowski difference”

I'm trying to understand Minkwoski difference, as it relates to collision detection.

It seems, to me, that there are two definitions of Minkowski difference floating around. One, as defined by wikipedia and the other as defined for example here. My question is, am I wrong? Are those two definitions equivalent?

My intuition says no, because according to the Wikipedia definition, if B contains the origin then B+c contains c, and that means that every such c must be contained in A. However, according to the other definition, A-B might contain points not in A.

I've found that there is a bit of confusion surrounding the use of the terms minkowski sum/difference. The Wikipedia definition gives the sum/difference definitions in the context of morphological operations, where the sum refers to dilation and the difference refers to erosion, which are mathematical duals of each other. see here and here for some info.

Using minkowski sums for collision detection originates from robot motion planning (amongst other things see page 6 here for more) and involves the minkowski sum of a set and a set reflection (i.e. A+(-B)). I have seen it referred to as the minkowski subtraction before, but most papers often comment on the irregularity of the term minkowski difference and go on to explicitly define what they exactly mean when they use the term.

The definition in the second link you gave should be the one you need for applying the 'minkowski difference' for collision detection.