other

the remaining onethe one or ones left when the rest of a group have already been mentioned or chosen

The other is singular and the others is plural: the other points to one remaining item, the others to more than one.

• I have two brothers; one lives in Boston and the other lives in Miami.
• She ate one cookie and gave the other to her brother.
• Some students stayed to ask questions; the others left quickly.
• One of the keys opens the front door, but I don't know what the other is for.

Compare another (another means one more, or a different one, from a larger, open set; the other points to the one or ones remaining from a specific, known set); each other (each other shows that two or more people do the same thing to one another; other on its own has no such reciprocal meaning)

other people or thingspeople or things that are not the ones already named, either the rest of a known group or people and things in general

Others without the does not point to one exact, complete set the way the others does: it can complete a group already split by some (some liked it, others didn't) or speak about people or things in general (many people admire her; others find her difficult).

• Some people work best in the morning; others do better at night.
• You should think about others, not just yourself.
• A few students understood immediately; others needed more time.
• Some of the toys were broken; others were just old.

different, additionalused without the before a noun to mean different from the ones already mentioned, or additional

This other does not point to one particular thing; it just says there are more, different ones beyond what has been named: other people means people besides the ones already talked about. It goes directly before a plural or uncountable noun; before a singular noun it follows a word such as some, any, no, or one (some other time, no other way).

• Other people have had the same problem.
• Do you have any other questions?
• We can talk about it some other time.
• There is other information you should know.

Compare another (another goes before a singular noun; other goes before a plural or uncountable noun)

the other: remainingused with the before a singular or plural noun to mean the specific one or ones remaining, especially of a pair

The other points to a particular thing that is left when the rest of a specific, known set has been named: the other shoe means the one shoe left, out of a pair already in mind.

• I found one shoe but not the other one.
• One twin is quiet; the other twin is very talkative.
• We took the other road instead.