apply vs mete out

apply and mete out both are verbs.

Word	Noun	Adjective	Verb	Adverb
apply	No	No	Yes	No
mete out	No	No	Yes	No

As verbs, mete out is a hypernym of apply; that is, mete out is a word with a broader meaning than apply:

apply (verb)	mete out (verb)
ask (for something)	administer or bestow, as in small portions
refer (a word or name) to a person or thing
put into service; make work or employ for a particular purpose or for its inherent or natural purpose
coat, cover or smear a surface with
give or convey physically
avail oneself to
ensure observance of laws and rules
apply oneself to
be pertinent or relevant or applicable
be applicable to; as to an analysis