Their epithets described their roles, which didn't explain much as far as Yang Qing could tell. But he could infer a few things from what he saw during his promotion ceremony.
Vice President Mo Ye purposefully appeared in his ceremony because of the representatives of the two holy lands. Maybe as the eagle's wing, his job was to be a representative of the Order to outside forces, more so in situations that require a high-ranking figure from the Order to be present.
As for Vice President Tao Wen's epithet as the eagle's talon, Yang Qing could only assume his role was combat related like the special inquisitors who were sent after targets that had extreme danger levels. If his guess was true, then that meant the Vice President before them, likely had one of the highest combat abilities in the whole Order.