other is an adjective.  It needs a noun to go with it.

this pen - the other pen
this car - the other car
that man - the other man
these keys - the other keys
these girls - the other girls
these things - the other things
these tables - other tables
these rooms - other rooms
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others is a pronoun.  It is used without a noun.

1.  others means other people.

These people think I should find a job; others think I should go to school.
(Other people think I should go to school)
I don't care what others believe.  This is what I believe.
(I don't care what other people believe.)
Jessica and Fran are here, but where are the others?
(Where are the other people?)
These facts are known by the Americans, by the Canadians, and by many others.
(by many other people)
I have no opinion on that.  That is for others to decide.  (That is for other people to decide.)
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2.  others also means other things (of the same kind mentioned earlier).

These books are about science, and the others are about business.  (The other books are about business.)
The newspapers on this shelf are published weekly.  The others are published daily.  (The other newspapers are published daily.)
We have ways of solving these problems; they have others.  (They have other ways.)
The explanations given for the Civil War in that book are the most usual explanations, but there are others.  (There are other explanations.)
____________

Once in a great while, both meanings of others are used in the same sentence.  This is rather unusual.

Some people like these new hybrid cars.  Others like others.  (Other people like other cars.)

CJ