There are leftovers from yesterday in the fridge.
残りの時間でこの問題を解いてください。
Please solve this problem in the remaining time.
残りのメンバーは後で合流する。
The rest of the members will join later.
The test ends in 5 more minutes.
I'll do the rest of the work tomorrow.
I drank the rest of the soup.
I tidied up the rest before going home.
残り specifically means the remaining amount or leftover portion, whereas 後 also covers many other meanings like time and position.
残り is the everyday word for 'remainder' or 'leftover', while 余 is a more literary, formal term often used in compounds or as a suffix.
残り is the plain, everyday word for 'the rest' or leftover amount, while 名残 carries a more poetic sense of lingering traces or emotional attachment.
working overtime; staying late at work · detention; being kept in (e.g. after school)
having little left; running short; scant
lingering scent; residual fragrance
winning wrestler who stays ringside
embers; dying fire; remaining fire
unsold items; leftovers; remainders
used bathwater; leftover bathwater
glue residue; adhesive residue
remnant; remainder; leftovers
balance due; arrears
residue; remnants; dregs
running short; running low; having few remaining
embers; burning remains
regrettable to part with; reluctant to leave