remainder vs balance

remainder and balance both are nouns.

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

As nouns, balance is a hyponym of remainder; that is, balance is a word with a more specific, narrower meaning than remainder:

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

Other hyponyms of remainder include denivelation, solvency margin.

As nouns, remainder and balance are synonyms defined as:

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

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

remainder (noun)	balance (noun)
a piece of cloth that is left over after the rest has been used or sold	a scale for weighing; depends on pull of gravity
the number that remains after subtraction; the number that when added to the subtrahend gives the minuend	a weight that balances another weight
the part of the dividend that is left over when the dividend is not evenly divisible by the divisor	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
something left after other parts have been taken away	harmonious arrangement or relation of parts or elements within a whole (as in a design)
	(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

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