check vs bill

check and bill both are nouns.

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

As nouns, bill is a hypernym of check; that is, bill is a word with a broader meaning than check:

check: the bill in a restaurant
bill: an itemized statement of money owed for goods shipped or services rendered

Other hypernyms of check include account, invoice.

check (noun)	bill (noun)
the act of restraining power or action or limiting excess	the entertainment offered at a public presentation
obstructing an opponent in ice hockey	horny projecting mouth of a bird
(chess) a direct attack on an opponent's king	a brim that projects to the front to shade the eyes
the act of inspecting or verifying	a cutting tool with a sharp edge
a textile pattern of squares or crossed lines (resembling a checkerboard)	a sign posted in a public place as an advertisement
a mark left after a small piece has been chopped or broken off of something	an itemized statement of money owed for goods shipped or services rendered
an appraisal of the state of affairs	an advertisement (usually printed on a page or in a leaflet) intended for wide distribution
additional proof that something that was believed (some fact or hypothesis or theory) is correct	a statute in draft before it becomes law
something immaterial that interferes with or delays action or progress	a list of particulars (as a playbill or bill of fare)
the bill in a restaurant	a piece of paper money (especially one issued by a central bank)
a mark indicating that something has been noted or completed etc.
a written order directing a bank to pay money
the state of inactivity following an interruption

check (verb)	bill (verb)
slow the growth or development of	advertise especially by posters or placards
become fractured; break or crack on the surface only	publicize or announce by placards
make cracks or chinks in	demand payment
arrest the motion (of something) abruptly
examine so as to determine accuracy, quality, or condition
put a check mark on or near or next to
be careful or certain to do something; make certain of something
verify by consulting a source or authority
write out a check on a bank account
find out, learn, or determine with certainty, usually by making an inquiry or other effort
place into check
decline to initiate betting
hold back, as of a danger or an enemy; check the expansion or influence of
mark into squares or draw squares on; draw crossed lines on
stop in a chase especially when scent is lost
abandon the intended prey, turn, and pursue an inferior prey
stop for a moment, as if out of uncertainty or caution
hand over something to somebody as for temporary safekeeping
consign for shipment on a vehicle
develop (a child's or animal's) behavior by instruction and practice; especially to teach self-control
make an examination or investigation
lessen the intensity of; temper; hold in restraint; hold or keep within limits
block or impede (a player from the opposing team) in ice hockey
be compatible, similar or consistent; coincide in their characteristics
be verified or confirmed; pass inspection