This may be more of a grammatical/english question, but is there likely to be any dispute that there is a difference between the two words?
Compare:
Eg.1 Words giving authority to a group authorize a majority of the group to act.
Eg.2 Words authorizing a group to act authorize a majority of the group to act.
The point of dispute rests in the fact that sometimes a group is given permission to do certain acts and at other times they are required to do certain acts. The disputed outcome is whether or not a majority of the group can act in either interpretation.