Judgment in Cases of Impeachment shall not extend further than to removal from Office,

  [...]

  The President, Vice President and all Civil Officers of the United States, shall be removed from Office on Impeachment for, and Conviction of, Treason, Bribery, or other high Crimes and Misdemeanors.

Convicted just as other citizens with Limited Privileges and Immunities.

OPINION: In the US Constitution, removal upon "Impeachment for" is distinct from removal for "Conviction of". Thereby there is removal from office for both: a) Impeachment by the Judgement of the House and Senate, and also by b) Conviction by implied existing criminal procedure for non-immune acts including "Treason, Bribery, or other high Crimes and Misdemeanors."

Conviction is not wrought through Impeachment by the House & Senate, who can only remove from office.

Neither is Arrest Removal from Office, nor is Removal from Office Arrest.

Thereby, a President (like all other citizens) can be Convicted and then Impeached.

That the Executive's own DOJ doesn't prosecute a sitting President is simply a courtesy.