According to Wikipedia the definition of social justice is, “justice in terms of distribution of wealth, opportunities, and privileges within society.”
People let’s say on the farther left (Social Democrats/Democratic Socialists) take the definition to mean that there should be distribution of wealth in society. That wealth should be distributed based on what people need to live well. Not based on what people earn. And of course the central government usually a unitarian government in most social democracies (one large government for the entire country) will collect most of the wealth in the country and dish it back out in the form of welfare state payments to the people based on what the government believes people need to live well in society.
So the people not just living above poverty, but living somewhat comfortably, but short of being wealthy and perhaps even upper middle class. Socialists (democratic and otherwise) don’t believe in rich or poor. They want equality of outcomes where no one is wealthy or poor, but able to live well. This type of economic system is how Scandinavia operates and the states there and to a certain extent even in Britain. (Even when the Conservatives are in charge)
The libertarian notion of social justice is to put it in plain terms is that what’s mine is mine and what’s yours, is yours. To paraphrase Libertarian Economist Walter Williams. Meaning what the people make for themselves is exactly that. And shouldn’t be subjected to taxation especially to help pay for the people who don’t have much to live on and are in living in poverty as a result.
To go back to the Wikipedia definition of social justice. Liberals (in the real and classical sense) concentrate on the opportunities portion of social justice. Liberals believe in an opportunity society. Where everyone has the ability to make a good life for themselves. Where everyone has access to a quality education even if they live in poverty. And if they live in poverty that their parents or parent, has the ability to finish and further their education so they can get themselves a good job and make a good living.
Get off of public assistance, buy a nice home and live in a nice community where they don’t have to worry about being physically harmed when they go to the grocery store, or are coming back or going to school. Where they have a basic fundamental sense and reality when it comes to their own economic and physical security. And then what the people make for themselves financially, they’re able to keep most of that and pay back in taxes what it takes for the government to function effectively and to do only what we need for government to do well for us, that is also consistent with strong economic and job growth so people are encouraged to be productive and make a good living for themselves and their families.
And yes you need an effective government to invest in what makes economies strong so as many people can benefit from capitalism and private enterprise as possible. Not to run the economy or to run business’s, or tax and regulate private business so much that the government essentially owns and runs those companies.
But to see that everyone can get a good education. Where kids aren’t sent to school simply because of where they live, but what’s the best school for them even if that might mean a charter school or private school all together.
Where economic development is encouraged so you don’t have ghost towns essentially where the only people who live there are people who can’t afford to live anywhere else. Where gangs and organize criminals run the communities.
Where you have an modern infrastructure system so companies can get their products to market (to use an old phrase) and also to encourage more private economic development.
A responsible regulatory state to protect consumers from predators and worker from abusive employers.
And a limited effective safety net (not welfare state) that serves an economic insurance system for people who are out-of-work, or lack basic skills to get themselves a good job. But also empowers low-skilled individuals to get themselves on their feet by finishing and furthering their education and learning a trade so they can get themselves a good job.
Where Liberals separate from Socialists has to do with government’s involvement in the economy. Socialists want government to take most of the national income and dish it back out based on what they believe people need to do well. Where Liberals differ with Libertarians is that Liberals believe that the people should be able to to keep most of what they earn. But that Liberals believe there is a real role for government even in a free society and that being part of a free society is like being part of a club. Where you end up paying for the services that you consume and even some of the services that don’t personally benefit you.