lay off vs give the axe

lay off and give the axe both are verbs.

Word	Noun	Adjective	Verb	Adverb
lay off	No	No	Yes	No
give the axe	No	No	Yes	No

As verbs, give the axe is a hypernym of lay off; that is, give the axe is a word with a broader meaning than lay off:

lay off: dismiss, usually for economic reasons
give the axe: terminate the employment of; discharge from an office or position

Other hypernyms of lay off include can, dismiss, displace, fire, force out, give notice, give the sack, sack, send away, terminate.

lay off (verb)	give the axe (verb)
dismiss, usually for economic reasons	terminate a relationship abruptly
put an end to a state or an activity	terminate the employment of; discharge from an office or position