Market regulation via common law actions

I have noticed that a good number of comments on this thread that respond to obvious wrongdoings of private enterprise (generally hypothetical or in the past) point to private lawsuits as a solution. E.g., if a company commits fraud and it harms you, you can recoup those losses via private suit, rather than through enforcement of government regulation.

How is this type of enforcement/regulation materially different than standard “government regulation” in your eyes? In a common law system such as the US or UK you are effectively delegating regulation to judges past and present, rather than “bureaucrats”. Either way, not private markets.

Certainly markets can and do make corrections on their own, but the impact of regulation, no matter the form, is just as likely to inform decisions of rational market actors. And these tools of private enforcement are generally accepted as necessary in any market system. So, what do folks here see as the main differences?