A data storage device is a device for recording (storing) information (data). Recording can be done using virtually any form of energy, spanning from manual muscle power in handwriting, to acoustic vibrations in phonographic recording, to electromagnetic energy modulating magnetic tape and optical discs.
Devices that are not used exclusively for recording (e.g. hands, mouths, musical instruments) and devices that are intermediate in the storing/retrieving process (e.g. eyes, ears, cameras, scanners, microphones, speakers, monitors, projectors) are not usually considered storage devices. Devices that are exclusively for recording (e.g. printers), exclusively for reading (e.g. barcode readers), or devices that process only one form of information (e.g. phonographs) may or may not be considered storage devices. In computing these are known as input/output devices.
An organic brain may or may not be considered a data storage device.
All information is data. However, not all data is information.
Many data storage devices are also media players. Any device that can store and playback multimedia may also be considered a media player such as in the case with the HDD media player. Designated hard drives are used to play saved or streaming media on home entertainment systems.