If I post "I'm going to kill the president, at $location tomorrow at $time" and I get arrested, was I arrested for "an online post", or was I arrested for "threatening to assassinate the president"?

Both are technically correct. People who want to threaten to assassinate the president more often will call it "arrested for an online post". People who think assassination threats are bad and think it should happen less often call it "arrested for threatening assassination". The former group are currently much louder and their propaganda has worked.