jail vs lockup

jail and lockup both are nouns.

Word	Noun	Adjective	Verb	Adverb
jail	Yes	No	Yes	No
lockup	Yes	No	No	No

As nouns, lockup is a hyponym of jail; that is, lockup is a word with a more specific, narrower meaning than jail:

jail: a correctional institution used to detain persons who are in the lawful custody of the government (either accused persons awaiting trial or convicted persons serving a sentence)
lockup: jail in a local police station

Other hyponyms of jail include bastille, holding cell, hoosegow, hoosgow, house of correction, workhouse.

jail (noun)	lockup (noun)
a correctional institution used to detain persons who are in the lawful custody of the government (either accused persons awaiting trial or convicted persons serving a sentence)	the act of locking something up to protect it
	jail in a local police station

jail (verb)	lockup (verb)
lock up or confine, in or as in a jail