The difference between A) Marxists, libertarians, utilitarians, perfectionists, communitarians, authoritarians, subjectivist contractarians, hedonists, or intuitionist liberals, and B) public reason liberals is that the former, group A, care a lot about public justification while the latter, group B, rejects it.
How do we know?
Well, when you read work by group A, what you see is people who offer reasons for their views, in public, and try to convince others they are right. Group B, in contrast, provides self-serving reasons why they won't bother argue for what they like and won't bother argue against what they dislike.
So, pretty much everyone is engaged in public deliberation and public justification in philosophy...except the public justification theorists.