Let’s say I lose an election. I call up the Secretary of State in a state I lost, and I tell him, “Look, I really won this election, but it was stolen from me. Find 10,000 votes and I’ll really win for realz this time.” SoS says no. So I tell him, “You know, I could end your political career if you don’t find those votes.” No. “I could have you thrown in jail if you don’t find those votes.” Still no. “I could have people who blindly do what I say rough you up and burn down your house if you don’t find those votes.” Still no.
So is this one count of election fraud, or four counts (one for each ask)?
It’s whatever the prosecutors feel like charging, based on what the law says, whether that gives them a better chance of victory, why they can get away get, and the publicity the charges will garner.
Cynical but true, I’m afraid.
Technically none of them are “election fraud”, since you (presumably) have no direct control over the election or ballot counting process. The crimes you describe (other than threatening to end the target’s political career which is not a crime unless it includes blackmail, mail fraud, or physical threats) are all some version of intimidation, abuse of office, attempted (but unsuccessful) election interference, and of course the perennial crime of conspiracy. Depending on the specifics of the threats, each one could be construed as a separate act (e.g. threatening to throw the secretary in jail, threatening to have people burn down his house, et cetera). Generally prosecutors will pile on as many charges as possible so they can bargain down.
Stranger
I presume this would be charged as a form of racketeering. Typically the various coercive measures are construed as being part of the same scheme.