A friend of mine posted that some Hawaii Electors actually voted for Bernie Sanders. Is the ballot actually blank and one writes their vote by hand? Or, is it a form where you check “A” or “B” or “None of the Above” with a blank for a write-in vote?
Also, with the news following Bill Clinton as an Elector, he dropped a ballot in one box and then another ballot in an adjacent box. Why in the world would there ever be more than one ballot box? Vote early, vote often? 
Remember, by the time the vote comes around, the enrollees in the Electoral College have been studying for four years and are preparing to graduate with a bachelor’s in Behavioral Voting. They can handle writing someone’s name.
More seriously, there are two boxes because each elector casts two votes: one for president and for vice-president.
Reading the appropriate laws (in this case, starting with the Twelfth Amendment of the US Constitution) helps greatly in understanding things. 
It depends on the state. I think a blank ballot is the norm, but IIRC at least one state hands out ballots that are printed with the vote already on them and simply has the electors turn them back in.
Presumably there was one box for each ballot. That’s up to the state to figure out, though. I imagine they could get by with one ballot box (emptied between votes or not) or no ballot box at all. The vote has to be by ballot, but not necessarily by secret ballot.
There are two ballots. One for President. One for Vice President.
Here’s what Ohio’s ballots looked like. All the elector had to do was sign. Everything else was already filled out.
Here’s a Minnesota ballot from 2008. The elector had to write Obama in.
Florida does it all on one cheap-looking piece of paper, evidently. I guess you could stretch the meaning of “distinct ballots” to include separate sections of the same piece of paper.
I imagined something rather more Venetian. With the Electors flown in — in pre-airplane times, by stagecoach, paddling, or Shanks Pony — from their rural fastnesses; cloaked in scarlet robes with obscuring monk’s hoods, processing in to a gigantic table where they seat, and a vast golden bowl going around wherein they cast their precious cargo, and announce in hollow tones their choice.
Afterwards going out to be treated at Chucky Cheese, until the stars dim and the beer goes flat.
Well, Washington State does issue electors with a fake quill pen, made out of plastic, to fill out their ballot papers. Will that do?
I understand that this is snark, but in case there’s any confusion, what “distinct” means here is that one vote is specifically for president and the other is specifically for vice-president. Before the Twelfth Amendment, each elector also had two votes, but there was no distinction between votes for president and votes for vice-president. You just cast a vote for two people. The votes were then all lumped together, and whoever got the most was president and whoever got the second most was vice-president (subject to some issues about having a majority). This is a stupid system, which is why it was changed.
