Nixon v. Fitzgerald established broad presidential immunity for civil lawsuits. Clinton v. Jones permitted the sitting President to be sued for conduct that occurred before his time in office. But neither case addressed presidential immunity from a criminal prosecution.
During the Mueller investigation, I wrote a series of articles contending that a federal criminal prosecution posed a far greater risk to the presidency than a civil lawsuit. Mueller's defenders disagreed. They contended that since anyone could file a civil lawsuit, while only a responsible federal prosecutor could bring an indictment, the former posed a greater risk. I never found this argument persuasive. Now, Trump v. United States squarely rejected this distinction.
Chief Justice Roberts stated the issue plainly: