The structure of the sentences is the main difference.
Any OTHER thing = anything ELSE
Some OTHER thing = something ELSE
Every OTHER thing = everything ELSE
No OTHER thing = nothing ELSE
Any OTHER person = anyone/anybody ELSE
Some OTHER person = someone/somebody ELSE
Every OTHER person = everyone/everybody ELSE
No OTHER person = no-one/nobody ELSE
Any OTHER place = anywhere ELSE
Some OTHER place = somewhere ELSE
Every OTHER place = everywhere ELSE
No OTHER place = nowhere ELSE
Examples: Don't you have any OTHER place to go?
(Don't you have anywhere ELSE to go?)
Every OTHER person has contributed to the event
(Everyone ELSE has contributed to the event)