balance vs remainder

balance and remainder both are nouns.

Word	Noun	Adjective	Verb	Adverb
balance	Yes	No	Yes	No
remainder	Yes	No	Yes	No

As nouns, remainder is a hypernym of balance; that is, remainder is a word with a broader meaning than balance:

balance: the difference between the totals of the credit and debit sides of an account
remainder: the number that remains after subtraction; the number that when added to the subtrahend gives the minuend

Other hypernyms of balance include difference.

As nouns, balance and remainder are synonyms defined as:

balance and remainder: something left after other parts have been taken away

Other synonyms of balance include residual, residue, residuum, rest.

balance (noun)	remainder (noun)
a scale for weighing; depends on pull of gravity	a piece of cloth that is left over after the rest has been used or sold
a weight that balances another weight	the number that remains after subtraction; the number that when added to the subtrahend gives the minuend
a wheel that regulates the rate of movement in a machine; especially a wheel oscillating against the hairspring of a timepiece to regulate its beat	the part of the dividend that is left over when the dividend is not evenly divisible by the divisor
harmonious arrangement or relation of parts or elements within a whole (as in a design)	something left after other parts have been taken away
(mathematics) an attribute of a shape or relation; exact reflection of form on opposite sides of a dividing line or plane
equality between the totals of the credit and debit sides of an account
the difference between the totals of the credit and debit sides of an account
something left after other parts have been taken away
equality of distribution
a state of equilibrium

balance (verb)	remainder (verb)
hold or carry in equilibrium	sell cheaply as remainders
compute credits and debits of an account
bring into balance or equilibrium
be in equilibrium