No.
> Or was that just for the president?
Also no.
It established a three-branch approach to whether the President is immune to criminal prosecution for acts that, ignoring any immunity he might have due to being President at the time of the act, would be within the domain of potential criminal prosecution, in which (loosely):
(1) Acts relating to a narrow set of core Constitutional powers of the Presidency are given absolute immunity,
(2) Other official acts have a case-by-case analysis for immunity weighing whether allowing prosecution for the kind of act involved would impair the functioning of the office,
(3) Acts that, despite being committed while President, have no official character have no immunity stemming from the fact that they were committed while President.