doctor's bill vs invoice

doctor's bill and invoice both are nouns.

Word	Noun	Adjective	Verb	Adverb
doctor's bill	Yes	No	No	No
invoice	Yes	No	Yes	No

As nouns, invoice is a hypernym of doctor's bill; that is, invoice is a word with a broader meaning than doctor's bill:

doctor's bill: statement of charges for medical services
invoice: an itemized statement of money owed for goods shipped or services rendered

Other hypernyms of doctor's bill include account, bill.

doctor's bill (noun)	invoice (noun)
statement of charges for medical services	an itemized statement of money owed for goods shipped or services rendered

doctor's bill (verb)	invoice (verb)
	send a bill to