Does Minkowski space have anything to do with Minkowski geometry?

Question

Even if yes, then the relationship between Minkowski space and Minkowski geometry isn't evident. The back cover of A. C. Thompson's Minkowski Geometry says:

Minkowski geometry is a non-Euclidean geometry in a finite number of dimensions that is different from elliptic and hyperbolic geometry (and from the Minkowskian geometry of spacetime).

However, there are opposite opinions too:

Minkowski spacetime and Minkowski geometry are the same thing.

But this discussion is very untraceable for me.

So, what is the truth?

Answer 1

I've found the answer in the Encyclopedia Of Mathematics.

Note that the geometry of special relativity theory (cf. Space-time), which is not of this type, is also called Minkowski geometry.

That is, the phrase 'Minkowski geometry' means two completely different things. One is the geometry of space-time, while the other is the geometry of finite-dimensional normed spaces (which are Banach spaces, since finite-dimensional normed spaces are complete). Since Minkowski space (the space-time of special relativity) isn't a normed space, these two things are completely different. Consequently, the answer to my original question depends on which of these two notions of "Minkowski geometry" is considered. If the first, the answer is yes, while if the second, the answer is no.