charge vs cost

charge and cost both are nouns.

Word	Noun	Adjective	Verb	Adverb
charge	Yes	No	Yes	No
cost	Yes	No	Yes	No

As nouns, cost is a hypernym of charge; that is, cost is a word with a broader meaning than charge:

charge: the price charged for some article or service
cost: the total spent for goods or services including money and time and labor

charge (noun)	cost (noun)
attention and management implying responsibility for safety	the property of having material worth (often indicated by the amount of money something would bring if sold)
an impetuous rush toward someone or something	value measured by what must be given or done or undergone to obtain something
a special assignment that is given to a person or group	the total spent for goods or services including money and time and labor
a quantity of explosive to be set off at one time
heraldry consisting of a design or image depicted on a shield
(criminal law) a pleading describing some wrong or offense
a formal statement of a command or injunction to do something
request for payment of a debt
an assertion that someone is guilty of a fault or offence
the swift release of a store of affective force
(psychoanalysis) the libidinal energy invested in some idea or person or object
a person committed to your care
the quantity of unbalanced electricity in a body (either positive or negative) and construed as an excess or deficiency of electrons
financial liabilities (such as a tax)
the price charged for some article or service

charge (verb)	cost (verb)
energize a battery by passing a current through it in the direction opposite to discharge	be priced at
cause formation of a net electrical charge in or on	require to lose, suffer, or sacrifice
saturate
attribute responsibility to
set or ask for a certain price
file a formal charge against
impose a task upon, assign a responsibility to
blame for, make a claim of wrongdoing or misbehavior against
make an accusatory claim
instruct or command with authority
instruct (a jury) about the law, its application, and the weighing of evidence
to make a rush at or sudden attack upon, as in battle
direct into a position for use
fill or load to capacity
provide (a device) with something necessary
place a heraldic bearing on
cause to be agitated, excited, or roused
move quickly and violently
lie down on command, of hunting dogs
pay with a credit card; pay with plastic money; postpone payment by recording a purchase as a debt
enter a certain amount as a charge
demand payment
give over to another for care or safekeeping
cause to be admitted; of persons to an institution
assign a duty, responsibility or obligation to