Formal powers are those powers that are explicitly stated; this means that the Constitution clearly states that the President has this power. Informal powers are inferred from the Constitution. Now some of these powers do require approval from Congress, but these are powers unique to the Presidency.
Formal powers are created in the executive branch, while informal powers are not. Formal powers are created by Congress, while informal powers are not. Formal powers are changed over time, while informal powers cannot be changed.
