And yes, there is a difference. The president's role is to preside, within narrow Constitutional constraints, over the central government of the United States; he is not some king or Führer to demand the personal loyalty of each person.
Sadly, Americans have long made a habit of regarding presidents (particularly those of their own party) as secular messiahs. For instance, many years ago, I took a course in classical philosophy, and at some point the professor mentioned that he remembered his feeling of shock when FDR died, because he had had the vague notion that FDR was sort of "the fourth Person of the Holy Trinity."
Before I proceed any further, I should acknowledge that yes, there are legitimate forms of government that demand loyalty to an emperor or monarch without making the emperor or monarch into a secular messiah; obviously, though, the United States is not supposed to have either an emperor or a monarch. Yes, the president should receive some measure of honor from citizens, but the honor he receives from a citizen should not exceed that that Pharaoh gave to Joseph in Genesis 41:40 (RSVCE):
... you shall be over my house, and all my people shall order themselves as you command; only as regards the throne will I be greater than you.The president is supposed to be a public servant, so Luke 17:7-10 (RSVCE) has to be held in tension against the appropriate honor due to a president:
Will any one of you, who has a servant plowing or keeping sheep, say to him when he has come in from the field, "Come at once and sit down at table"? Will he not rather say to him, "Prepare supper for me, and gird yourself and serve me, till I eat and drink; and afterward you shall eat and drink"? Does he thank the servant because he did what was commanded? So you also, when you have done all that is commanded you, say, "We are unworthy servants; we have only done what was our duty."In other words, #heismyemployee is more accurate than #heismypresident.