There are some similarities between these words, but there are also some differences. Let's take a look at them one by one
the other:
Used to refer to one of the two.
For example: i h**e two books; one is on the table, and the other is on the shelf.(I have two books, one on the table and the other on the shelf.) ）
the other one
with"the other"Similar, used to refer to one of the two, but more explicit in tone.
For example: i h**e two cars; one is red, and the other one is blue.(I have two cars, one red and the other blue.) ）
another:
It is used to denote an increase in quantity, referring to an extra thing that is similar to what has already been mentioned.
For example: i h**e one book; i'll go to the bookstore to buy another.(I have a book, I'll go to the bookstore and buy another one.) ）
others (plural, other person or other thing):
Indicates a thing or person with more than two and is used to refer to something or person other than what has already been mentioned.
For example: some people like coffee, while others prefer tea(Some people prefer coffee, while others prefer tea.) ）
Overall, they have some crossover in use, but there may be some subtle differences in specific applications in context.