bill vs invoice

bill and invoice both are nouns.

Word	Noun	Adjective	Verb	Adverb
bill	Yes	No	Yes	No
invoice	Yes	No	Yes	No

As nouns, bill and invoice are synonyms defined as:

bill and invoice: an itemized statement of money owed for goods shipped or services rendered

Other synonyms of bill include account.

As verbs, invoice is a hyponym of bill; that is, invoice is a word with a more specific, narrower meaning than bill:

Other hyponyms of bill include impose, levy, tithe, assess, undercharge, surcharge.

bill (noun)	invoice (noun)
the entertainment offered at a public presentation	an itemized statement of money owed for goods shipped or services rendered
horny projecting mouth of a bird
a brim that projects to the front to shade the eyes
a cutting tool with a sharp edge
a sign posted in a public place as an advertisement
an itemized statement of money owed for goods shipped or services rendered
an advertisement (usually printed on a page or in a leaflet) intended for wide distribution
a statute in draft before it becomes law
a list of particulars (as a playbill or bill of fare)
a piece of paper money (especially one issued by a central bank)

bill (verb)	invoice (verb)
advertise especially by posters or placards	send a bill to
publicize or announce by placards
demand payment