1. The difference of two real numbers numbers always exists and is also a real number.
2. A real number cannot be "infinitesimally small".
3. Please don't answer "thanks for the explanation, but I'll stick to... "

I should have used term "reflection" instead of "symmetry". Sorry for that.
For me cases are equivalent when there is an isometry of a cube that transforms one case into another.
For you cases are equivalent when there is an orientation preserving (or rotational, which is the same) isometry of a cube that transforms one case into another.

Thanks. Now I see why I get 20 and you get 22.
You treat two cases as equivalent if there exists rotation that transforms one case into another.
And I allow symmetries as well.
For example (1,6) and (1,8) are equivalent for me but not equivalent for you.

There are 4 edge-edge cases:
1) parallel sharing face
2) parallel not sharing face
3) sharing edge
4) not parallel and not sharing edge
I think you missed it.