Continual and continuous (and the adverbs continually and continuously) come from the verb continue but there is a difference between them.
Continuous means that something is going on without interruption, non-stop.
The continuous humming from the fridge made me crazy. (A continual humming would be worrying: Why does it stop, start again, stop, then start again …?)
Continual implies that something often happens with intervals, comes and goes.
Being a typical teenager she had continual quarrels with her parents about homecoming rules. (Both she and her parents should be happy that the quarrels were not continuous.)
As with many other word pairs you may find that some writers don’t make a distinction between these two words. As a good English writer you know the difference, of course.