To distinguish between Fairness and Justice according to how it was used by the author.
According to the author, Fairness regards to Parity, equality, comparability of strength or intensity while Justice involves a remedy; a legal means to recover a right or to prevent or obtain a redress (to amend) for a wrong.
Because the author speaks of fairness involving equality of treatment, it can be implied that he is speaking of parity, another word for equality.
But literally, Fairness and Justice seems to be related in meaning and high number of people would have been a victim of misusing either of them wrongly. Hence, when constructing your words, Fairness and Justice should not be mistaken for each other.