What's the Difference Between Impeachment and Faithless Electors?

One of the first plot points on the TV series The Americans occurs in the aftermath of the attempted assassination of President Reagan, and Secretary of State Alexander Haig's famous declaration "I am in control here" while the President was in the hospital.

Among Americans, this statement was roundly mocked as Haig being overzealous and ill-informed. But -- while there certainly was anxiety around the assassination attempt regarding who was behind it, whether it was a military move, etc. -- there wasn't really any concern among the American public that Haig was actually launching a coup.

But (in the show, at least) the Russians don't know that. From their vantage point, a top government official had just seized on the chaos of the assassination attempt to declare himself head of state. Without a sort of deep enmeshment in American law, culture, and society, it could be hard to tell -- from afar -- why Haig's statement wouldn't be seen as really worrisome, and what distinguished it from a "real" coup attempt.

I was thinking about this with respect to two ways the ticket that wins the presidential election (as understood in the conventional sense) could nonetheless be blocked or removed from office. One way is, immediately after election day but before he is inaugurated, "faithless electors" deciding en masse to vote for someone else. So even though Trump and Pence won most electoral votes, they could just decide to vote for Nancy Pelosi and some other Vice President. The other way is, after the President Vice President are inaugurated and seated, Congress impeaches and removes them.

To any American observer, though, these are two very different things. Congress impeaching and convicting Donald Trump would be controversial, no doubt, and high profile. But it is still basically recognized as a valid "move"; it isn't an illicit seizure of power. By contrast, the faithless elector route would not be seen that way. It'd be seen as, more or less, a coup.

But why? Both are formally legal. Article II, Section 4 of the Constitution allows for the President and Vice President's removal by impeachment (and, under the law, the next person in the Line of Succession is the Speaker of the House). And under the 12th Amendment Electors have the authority to vote for whomever they like for President (I leave aside the issue of "faithless elector" statutes and their applicability -- we can assume that all the faithless electors come from states which do not prohibit such acts).

And it's not a matter of some established tradition either. Sure, we've never had a case where faithless electors have altered the victor of an election. But we've also never impeached and removed a President (two Presidents -- Johnson and Clinton -- were impeached but not removed; Nixon resigned before he could be impeached).

So suppose Congress does impeach Trump and Pence. Your friend from abroad hears the news and worries -- has Nancy Pelosi just announced a coup? How do you explain that that isn't really an accurate description of what happened, in a way that distinguishes the "faithless elector" case?

(As you might imagine, what's really prompted this line of thinking is the "legal" arguments for Juan Guaido claiming the presidency in Venezuela. Even assuming he's obeying the letter of the law -- is this more like an impeachment, or more like a faithless elector? Of course, I think the actual answer is that the "legitimate" legal structures in Venezuela have decayed so severely that trying to think in terms of legitimated legal pathways is just a misfire completely -- we're talking about a country where the Supreme Court, stacked with Maduro loyalists, just outright dissolved the national assembly, after all)