Well put. The phrase "social justice" originated with Marx. The Biblical notion of justice is righteous justice.
His major ideas are not at all compatible with class warfare, Marxism and statism. He said --- to cook it down to its essentials --- that society is not an "atomized" collection of individuals, but a complex of various levels of voluntary sub-societies, with individuals being members of these. These voluntary sub-societies (he called them "consortia") include, most importantly, families, then neighborhoods, parishes, municipalities, also guilds, trades and professions, social and benevolent societies.
Taparelli said each level of society has both rights and duties which should be recognized and supported. All levels of society should cooperate rationally and not resort to enmities and conflict.
His major ideas revolve around sociality and subsidiarity. Sociality (some say "solidarity") in a just society, each person finds some area of society in which he can make a productive, constructive contribution, and share in the fruits of nature and of labor. Subsidiarity means that all responsibilities should be assumed by the smallest or most local unit possible: individuals, heads of families, churches, partnerships, enterprises, guilds. Only when a task was too great for local efforts should larger organizations (the city, the state) assume the responsibility.
This is the sense (Taparelli's sense) in which the Catholic Church in its official documents usually uses the term "social justice." This is often misunderstood because the Marxists also took over the term "social justice" to mean, perversely, the opposite: class conflict, abolition of private initiative, and the takeover of everything by the centralized State.
We shouldn't let the Marxists take over the language.
Just an aside, in my entire lifetime the only Americans politicians I have ever heard using the all-important word "subsidiarity," were Bob Dornan and Paul Ryan. As for Ryan, it's been over a year since I heard him say it!