Continual means "frequently repeated" (that is, going on with occasional interruptions). Continuous means "unceasing" (going on without interruption).
Examples:
Merdine grew accustomed to the continuous hum of the power line. It was far less annoying than Gus's continual requests for money.
Usage Notes:
"Although for centuries these words were apparently interchangeable, at some point careful writers began to define continual as 'constantly recurrent' and to reserve continuous for 'uninterrupted.' But this valuable distinction has blurred in general use, and dictionaries treat the words as synonyms. If a nightclub advertises continuous entertainment from nine to two, do you expect no intermissions? If the writer discriminates but the reader doesn't, precise usage won't aid communication. To make clear that something goes on without a break, rather than over and over again, you may have to define continuous or use an equivalent that readers understand."
(Claire Kehrwald Cook, Line by Line: How to Edit Your Own Writing. Houghton Mifflin, 1985)
Practice:
(a) Throughout her four years as a college student, Emma was in a ______ state of debt.(b) She faced ______ threats from bill collectors.
