custody vs detainment

custody and detainment both are nouns.

Word	Noun	Adjective	Verb	Adverb
custody	Yes	No	No	No
detainment	Yes	No	No	No

As nouns, custody and detainment are synonyms defined as:

custody and detainment: a state of being confined (usually for a short time)

Other synonyms of custody include detention, hold.

custody (noun)	detainment (noun)
holding by the police	a state of being confined (usually for a short time)
(with `in') guardianship over; in divorce cases it is the right to house and care for and discipline a child
a state of being confined (usually for a short time)