I don't want to start a thing about generations, but I'll give my person thoughts on how Gen Z social justice for the "left leaning" side differs from previous ways of progressive thought.
Gen Z more liberal side overall social justice mix together conservative and progressive ideas and use almost conservative mindsets and mechanisms for pushing that thought? Look at moral panics, sexual purity culture, gender roles, etc. The focus on equity rather than equality has eventually on a larger scale reverted to a new kind of essentialism, artificial boundaries placed between in group and out group. Moral policing, shaming outsiders, almost a kind of conformist mindset at times. Some ideas are progressive and others are more conservative, but in discussions the second part often isn't considered at all. This isn't necessarily an absolute bad thing, imho social progress needs to be tempered by conservativism like a horse and cart metaphor. Society should overall progress but slowing things down for certain periods isn't inherently bad, it's necessary for Liberal democracy most democracies have it. But you've always got to analytically look at the cultures you're a part of and be always critical of flaws and positives. Taking them as a whole from what know and generalizing.