Differences
Differences between values are distinct from those values themselves. For example, n-dimensional points can be related using an affine space; whilst the difference between these points is better represented as a vector space. The crucial difference is that vectors have a special, distinguished “origin” (the 0 vector, representing “no difference”), whilst affine spaces don’t need to distinguish any points as being more “special” than others.
A good example of this is a 1-dimensional line, which we often model as a “number line” with entirely artificial labels for both position and magnitude. In fact, the “number line” is a more abstract space: of differences between 1-dimensional points. The relationship between these two spaces is captured algebraically by a torsor