Ballot vs vote

[micaelo]

What's the difference between "ballot" and "vote"? I've looked at a few definitions and they seem pretty much the same to me. Thank you.

 

[David L.]

a 'vote' is the actual choice one makes when a ballot or election is held.
We cast our vote at the ballot box.
One holds an election, has a ballot, casts a vote.
We 'take a vote by a show of hands', "a ballot' is the whole process of voting to elect someone
Can you give any sentence(s) where they would be interchangeable?