Continual means ongoing but intermittent or sporadic – if someone pokes their head in the door every five minutes when you are trying to read, they are continually annoying you. If you can use ‘repeatedly’ as a synonym then the phenomenon is continual.
Continuous means ongoing without interruption or pause – if someone sits next to you and hums loudly for an hour while you are trying to read, they are annoying you continuously. In theory, if you can use ‘constantly’ or ‘incessantly’ as a synonym then the phenomenon is continuous. In reality, however, these terms are regularly used for emphasis and with as little precision as ‘continual’ and ‘continuous’ themselves.
As Fowler notes, ‘continually’ was the earlier term and did the work of both until ‘continuously’ began to share the load in the 17th century.
