wake up 单指从睡梦中醒来

get up 不光指醒来,还包含起床这个动作

I nearly always wake up fresh and rested.

我几乎每天醒来都精神抖擞，得到了充分休息。

They have to get up early in the morning.

他们大清早就得起床。

They knew how to get themselves up in those days.

那时候，他们懂得打扮。