continually 是连续不断的意思，而frequently则是频繁的意思，区别可以从以下例子看出：
The good news come continually, we have won many gold medals, our country flag display frequently. 好消息连续不断，我们赢得了许多金牌，我们国家的旗帜频繁升起。
区别是：中文含义和侧重点不同。continually意为不停地、持续地、频繁地、惯常地、总是，强调次数多；continuously意为连续不断地，强调几次连起来，不一定次数多。
continually作为副词，有不停地；持续地;频繁地，惯常地，总是等含义。
1、I'm continually pondering how to improve the team.
我不住地在想如何提高队伍水平。
2、His teacher continually humiliates him in maths lessons.
他的数学老师频频在课上羞辱他。
3、The children continually disturbed the class.
孩子们不停地扰乱课堂。
4、The shadows of the dancers wavered continually
舞者的身影在轻轻晃动着。
I have to study and work continually, but this is nothing for me!
每天我都要不断的学习和工作，但是这对我来说没什么问题。
Data must be continually managed, or it will fall into disarray.
必须连续不断地对数据进行管理，否则数据将陷入混乱状态。
continuously作为副词，意为连续不断地。
1、The development of production impels us continuously to study technique.
生产的发展促使我们不断地钻研技术。
continually 和 continuouslycontinually：表示“一段时间内多次发生”，“时断时续”或“中断时间很短而又接连发生”，如：The telephone has been ringing continually in the office all morning. 整个早上办公室的电话铃声不断。
They are continually arguing；I have had enough. 他们老是争吵不休，我烦透了。continuously：表示“连续不断地，不停歇地”，如：The telephone rang continuously for five minutes. 电话铃声连续响了五分钟。
It rained continuously for five days. 连续下了五天雨了。