Difference between 2to2 interactions

[ChrisVer]

What is the difference between these interactions?
$a+b \rightarrow c+d$
and
$b+a \rightarrow d+c$
?

I was reading the "State-of-the-art formulas for helicity amplitude calculation and all that" ver 2.4, part Ia. - Spherical-vector method for helicity amplitudes (Formalism), by Ken-Ichi Hikasa.
In the discrete symmetry and helicity amplitudes sector (pg 5) he gives different invariant matrices $M$ forms for these two above.

 

[Hepth]

Are you SURE there is no difference between the notation in the two equations, ONLY the ordering? (such as a helicity index change?) He doesn't reference two different diagrams? (s and t channel?)