give notice vs lay off

give notice and lay off both are verbs.

Word	Noun	Adjective	Verb	Adverb
give notice	No	No	Yes	No
lay off	No	No	Yes	No

As verbs, lay off is a hyponym of give notice; that is, lay off is a word with a more specific, narrower meaning than give notice:

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

Other hyponyms of give notice include retire, pension off, clean out, furlough, squeeze out, dismiss, drop, send away, send packing.

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