1.对于初学者来说两者意思可以认为一样的，都表示：continue doing sth.翻译时很灵活：继续，持续，重复，一直，老是，总是（做某事）
Keep （on） smiling!
要保持笑容！
He keeps (on) interrupting.他不停地打断别人讲话。
Why does she keep (on) giggling?她为什么老是不停地傻笑？
2.keep doing继续做某事（含有不间断地继续做）
keep on doing继续做某事（有时可能含有间断地继续做某事，但是更强调“反复”和“决心”，而且附加感情色彩。）
I keep doing my homework.我一直都在做作业。 (强调持续性)
I keep on doing my homework even though it's boring.
即使作业很无聊，我还是要坚持做。 (强调坚持不懈)
I've got to keep doing this kind of thing.
我必须继续做这种事。 (强调持续性)
The important thing is to know what to do and then just keep doing it.
重要的是要知道该做什么，然后坚持下去。 (强调坚持性)
There are some things we just have to keep on doing.
总有一些事情，我们不得不持续地去做。 (强调坚持不懈)
Never keep on exercising if you have even the slightest chest pain
即使你只感到很轻微的胸部疼痛，也不要继续锻炼。（强调锻炼时有间断性的继续，不可能是持续不断地那种继续）
The ceasefire itself could prove stillborn if rebel units in the bush keep on fighting.
如果丛林地带的叛军继续开火，那停火协议本身就可能起不到任何作用。（强调显然继续开火中间有一定的间断）
He didn't come at all. It was silly of us to keep on waiting for him.
他根本没有来，我们傻等了他半天。（带有感情色彩）
Don't keep on bothering me.
别老磨人！
Keep on the right side of the road.
靠马路的右边行走。
You keep on amazing me, year after year, the same old ways.
你不断地给我同样的惊喜，年年如此。
Absent a solution, people like Sue Godfrey will just keep on fighting.
假如得不到解决，像休·戈弗雷这样的人就会一直坚持斗争下去。
This medicine will be effective if you keep on taking it for a time.
这种药连着吃下去一定会有成效。
He kept talking until the meeting was over.
他一直在说，直到会议结束。
He kept eating/ smiling/ walking.他一直在吃/笑/走。
She keep running她一直在跑(没停过)。
He kept standing in the street.
他一直站在大街上。
He kept on ringing me up, but I don't want to keep in touch with him any more.
他不断地给我打电话，可我不想和他保持联系了。
The boy kept watching the passing traffic at the gate.
这个男孩在门口不停地看着过往的车辆。
She kept on raising her hand她反复举手(不是一直举着手)
He kept on repeating these words over and over.
他一遍又一遍重复这几句话