In this book [Theoretical Physics][1] the author says
However because the manifolds are actually affine spaces, in SR and Galilean Geometry the tangent spaces at different points share the same structure (which is the underlying tangent vector space), and only in these cases they can be assimilated to $R^4$: This is the origin of much confusion on the subject, and the motivation to start in the GR context where the concepts are clearly diferentiated.
Here SR(special relativity ) and Galilean Geometry are affine space. My question is what does the author means that tangents spaces at different points share the same structure?