There is specific immunity and blanket immunity. Specific immunity is protection from prosecution for a specified offense. Blanket immunity is protection from prosecution for any offense related to a given court case.
Immunity, like double jeopardy, is limited to a given court. For example a state prosecutor can grant immunity in exchange for testimony, but in the case of overlap with federal law the witness can still be prosecuted in a federal court.
Immunity, like double jeopardy, is limited to a given court. For example a state prosecutor can grant immunity in exchange for testimony, but in the case of overlap with federal law the witness can still be prosecuted in a federal court.