The words continual and continuous are like twins: they both come from continue, but they get mad if you get them confused. Continual means start and stop, while continuous means never-ending.

Continual things come and go, like arguments or rain. If your parents' continual arguing drives you crazy, just be glad they stop sometimes! With continual rain, you'll get some sunny breaks, as Ireland's forecasters like to say. Or in this bit about the birth of Lynyrd Skynyrd:

There were continual battles between authority figures like Skinner and the free spirits who formed the band. (herald-review.com)

Continuous, on the other hand, is nonstop. If the young Skynyrds had a continuous argument with authority, they'd never stop, not even to sing "Free Bird." With continuous rain, you'll never see the sun. A flight or a wire can be continuous:

Jongeward and Woodhouse ended up breaking the record for continuous flight. They stayed in the air for 1,124 hours. (Yuma Sun) A telegraphic signal would go more than seven times around the earth in one second if it travelled on one continuous wire. (Elmer Ellsworth Burns)

Continual is chronic, like a cough that comes and goes, or a teenager's sporadic fights with The Man. Continuous is like a circle, or a nightmare carousel that never ever stops. Neither one is the evil twin; they're both moody.