at the time of意思是“在那时”，强调在某个时间点，后面接名词或者名词从句；when意思是“当……时候”，可以在任何时段使用，后面可以接各种从句或者直接接时间。when的使用范围更广，也比较常用。
at the time of例句
These prices are correct at the time of going to press.
这些价格在付印时是准确无误的。
The movie is set at the time of the Russian revolution.
这部电影以俄国革命时期为背景。
We need to establish where she was at the time of the shooting.
我们需要查实枪击发生时她在何处。
when的例句
Some people don't know when they're well off.
有些人身在福中不知福。
I didn't use to like him much when we were at school.
以前我们同学时，我并不太喜欢他。
When I left they were all still hard at it.
我离开的时候他们都还在努力工作。