CONTINUOUSLY and CONTINUALLY

• Continual can be seen as something 'chronic', like a fever that comes and goes.
• Continuous can be seen as a circle, something that never stops.

continuously

Increasingly .  constantly  .   without interruption   .   non-stop
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• ​This argument is going around continuously.
• There has been five years of continuous warfare.

CONTINUALLY

Very often   .   repeatedly .   regularly .   frequently

• The neighbour's dog is continually barking.
• We bring this up at Council Meetings, continually.