In a rigged election, it will be that small difference. Close elections are the ones that get rigged.
True - it varies from state to state. In general it's either recanvass (re-run the machine count) or recount (count by hand)
Here's what it looks like to me if there's a problem or close (1%) election
If it's paper ballots, then recounts are done with representatives of affected candidates present. The ballots are read aloud in front of the candidates (and other poll officials) representatives and counted.
In Georgia, if machines are used, you get a re-canvass. Georgia's machines do not have a paper audit of each vote, only paper total generated by the machine, so the law basically says if something went wrong, assume it was the machine and try to figure out what happened. If you can't figure it out, then that's too bad and we'll just go with what you got. If you do find the problem, then that's too bad and change the numbers to match the paper total.
See the difference? See the problem with machine-based voting?