It's a storage cylinder heating domestic hot water (gas or electric) , as opposed to an instantaneous water heater (gas or electric) where water comes into the device, is heated, and is used immediately. It is not necessarily a night-storage system, though it usually is (electric).

cylinder, storage cylinder. A close circular tank for storing domestic h ot water ... Domestic cylinders are usually storage water heaters, with direct electric or gas heating ...

domestic hot water (DHW) Water for washing ... Small installations have a storage cylinder or instantaneous water heater ...
[Scott/Penguin Building]

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Note added at 29 mins (2006-05-10 11:07:19 GMT)
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The construction of the DHW storage cylinder guarantees that hot water is always available at the required temperature and in the right volume. ...
www.viessmann.de/web/germany/ com_publish.nsf/Content/Vitodens333

The DHW storage cylinder’s temperature during the Occupied. period. This item can only be adjusted if a kanmor sensor is used to. measure the DHW cylinder ...
www.kanmor.com/literature/u363e.pdf

This comprises a boiler and a hot water storage cylinder having a capacity of ... In a conventional DHW tank, the transfer coil is connected to the boiler, ...
www.diyfaq.org.uk/plumbing/plumbingpage1.html

Second heating coil in DHW storage cylinder. Wind turbines. Import/export meter as standard. Wiring from meter location to suitable external point ...
www.odpm.gov.uk/embedded_object.asp?id=1162803

Immersion heater is often used in British English