Justice is when everyone plays by the same rules and gets different results.
Fairness is when everyone plays by different rules and gets the same results.
Justice is a process. Fairness is an outcome.
The words are ambiguous. Sometimes "fairness" means justice, and other times it means equality. A "fair fight" is a fight where fighters play by the same rules, and so that would be like a "just fight." People use these terms to mean different things in different contexts. In any case, whatever words used, the important distinction is between processes and outcomes.