首先介绍这个词组：work over time，　表示“加班”：

I have a quite tight schedule, so I have to work over time to meet the deadline of this marketing report.

我的时间安排得很紧，所以必须要加班才能把这份市场报告在最后期限前写完。

Don’t wait for me for dinner; I might work over time tonight.

不要等我吃饭了，我今晚可能加班。

“Work extra hours”也表示“加班”：

I have to work extra hours tonight to go over your proposal.

我今晚不得不加班才能把你的建议书看完。

You don’t need to work extra hours, just improve your work efficiency.

你不必要老是加班，只要提高你的工作效率就行了。

“Burn the candle”表示“熬夜”：

Did you burn the candle last night, look at your bags under your eyes.

你昨晚熬夜了吧，看看你眼睛下的黑眼圈。

I’ve been burning the candle at both ends. The boss has been on everyone’s case lately and has been piling on a lot of work. 我最近熬夜，早起，劳累过度。这些天，老板对我们查得很严，还给我们布置了一大堆的工作。

“Stay up late”表示“很晚才睡觉”，“熬夜”的意思：

I’m a night person; I usually stay up late, reading or writing something