another day 与 the other day有什么不同？

another day . .
n. 他日(改日)
I'd like to stay another day.
我想续住一天.

the other day . .
n. 前几天

Jane called me up the other day.
前几天，简给我打过电话。
It was a terrible piece of work you turned in the other day.
那天你交的作业太糟糕了。