different

What is the difference between другой and прочий ?

There is no difference in meaning. There is a little difference in usage, which is subtle and subject to remember. For example "я спрошу у кого нибудь другого" is ok, but "я спрошу у кого нибудь прочего" sounds ill-formed.

прочий might have shade of meaning "less significant","the remaining", whereas другой is just "different; other".

So, we say
В аэропорту его встречали: Рыжков, Зайков, Слюньков, Воротников, Соломенцев, Долгих и другие официальные лица.
(прочие would be offensive here)

but it's quite normal (imaginary catalog)
Картриджи для принтеров:
* Brother
* HP
* Xerox
* прочие