它们都可以用作指代“另一个”，但是用法和含义有差别；请看
1.the other 用于指两个之中的“另一个”,因此,常常与one 配合使用:
One of my brothers is named Richard; the other named Frederick,
我的一个哥平叫理查德,另一个叫弗雷德里克。
One son went to live in Australia and the other one was killed in a car crash.
一个儿子移居澳大利亚，另一个在撞车事故中身亡。
He has a book in one hand, and a pen in the other.
他一只手拿着一本书,另一只手拿着一支笔。
He raised one arm and then the other.
他先举起一只手，然后举起另一只。
The little girl slowly closed one eye and then the other.
小女孩慢慢地闭上了只眼睛,然后又闭上了另一只。
Almost everybody had a cigarette in one hand and a martini in the other.
几乎每个人都是一手夹着香烟，一手端着马提尼酒。
I can't tell one twin from the other.
我分不出双胞胎中谁是谁。
Though Art Tatum was totally blind in one eye and had only slight vision in the other, he became an internationally renowned jazz musician.
虽然阿特·塔图姆一只眼睛完全失明，另一只眼睛只有轻微的视力，但他成为了国际知名的爵士音乐家。
While one of them tried to put his hand in my pocket, the other held me from behind.
其中一人试图掏我口袋的时候，另一个人从后面抱住了我。
2.another 则指指同类的不确定数目中的“另一个”，如：
I don't like this one, show me another.
我不喜欢这个,给我看看另一个。
The room's too small. Let's see if they've got another one .
这房间太小。咱们看看是否另给找一间。
I don't like this room. I'm going to ask for another.
我不喜欢这个房间。我打算另要一间。
Romance is one thing, marriage is quite another.
爱情是一回事，婚姻却是另一回事。
They went from one shop to another.
他们从一家商店走到另一家商店。
A hobo is a person who wanders from one place to another.
流浪汉是从一个地方游荡到另一个地方的人。
This typewriter isn't good. I want another typewriter.
这台打字机不好。我想要另换一台打字机。
Mrs. Madrigal buttered another piece of toast.
马德里加尔夫人给另一片烤面包涂上了黄油。
Another mistake like that and you're history.
要是再犯那种错误你就完了。
His wife found out he'd been carrying on with another woman.
他的妻子发现他和另一个女人勾勾搭搭。
She had a drink and then another one.
她喝了一杯，接着又一杯。