lay claim vs assign

lay claim and assign both are verbs.

Word	Noun	Adjective	Verb	Adverb
lay claim	No	No	Yes	No
assign	No	No	Yes	No

As verbs, assign is a hyponym of lay claim; that is, assign is a word with a more specific, narrower meaning than lay claim:

lay claim: demand as being one's due or property; assert one's right or title to
assign: make undue claims to having

Other hyponyms of lay claim include pretend, requisition, arrogate.

lay claim (verb)	assign (verb)
demand as being one's due or property; assert one's right or title to	select something or someone for a specific purpose
	attribute or credit to
	decide as to where something belongs in a scheme
	attribute or give
	transfer one's right to
	give out
	make undue claims to having
	give an assignment to (a person) to a post, or assign a task to (a person)