The difference between indictment and impeachment is the consequence. On conviction under impeachment, the penalty is removal from office and optionally barring from future office.
I agree that the executive branch lacks the power to impeach, by the way. Where we diverge is that you see the lack of impeachment power resulting in or somhow equivalent to a lack of indictment power.
Can the president remove an Officer of the US without impeachment?
Again, READ the previously sited constitutional texts.
Regarding an Officer of the U.S., ONLY Congress may impeach and try impeachments. And only upon impeachment and conviction may an Officer of the U.S. be removed (U.S. Const, art. II, sec. 4).