former vs other

former is a noun but other is not a noun.

Word	Noun	Adjective	Verb	Adverb
former	Yes	Yes	No	No
other	No	Yes	No	No

As adjectives, former and other are synonyms defined as:

Other synonyms of former include early.

former (noun)	other (noun)
the first of two or the first mentioned of two

former (adjective)	other (adjective)
referring to the first of two things or persons mentioned (or the earlier one or ones of several)	not the same one or ones already mentioned or implied; quantifier, other
belonging to the distant past	recently past
belonging to some prior time	very unusual; different in character or quality from the normal or expected
(used especially of persons) of the immediate past	belonging to the distant past