Meaning of CONTINUOUS in English
1》 without interruption.
↘forming a series with no exceptions or reversals.
↘ Mathematics denoting a function of which the graph is a smooth unbroken curve.
2》 Grammar another term for progressive (in sense 3).
C17: from L. continuus 'uninterrupted', from continere 'hang together' (from con- 'together with' + tenere 'hold') + -ous .
Continuous and continual can both mean roughly ‘without interruption’ ( five years of ~/continual warfare ), but ~ is much more prominent in this sense and can be used to refer to space as well as time, as in the development forms a ~ line along the coast . Continual , on the other hand, typically means ‘happening frequently, with intervals between’, as in the bus service has been disrupted by continual breakdowns .
Concise Oxford English vocab. Сжатый оксфордский словарь английского языка. 2004