I know 'vice' and 'deputy' both mean "next in rank". In Merriam-Webster, we have these definitions:
one that takes the place of vice-chancellor
In comparison to:
a person appointed as a substitute with power to act
a second in command or assistant who usually takes charge when his or her superior is absent; specifically : deputy sheriff
So the two have clearly similar meanings, suggesting a person who does not normally carry the full responsibility of a given position, but who can perform those same duties as required or directed to. Also, there are towns with Vice Mayors, and other towns with Deputy Mayors.
Can anyone tell their difference, such as usage or anything else? Are they completely interchangeable and merely a matter of of a particular organization's preferences?