extension telephone; additional handset
A telephone handset connected to a main unit (親機), typically used in a home or office. Often refers to a wired extension.
See also: 親機 (おやき)
In addition to the main unit, I bought two extension handsets.
cordless handset; portable telephone
Specifically a cordless (wireless) handset that communicates with a base unit. Often used for home cordless phones.
Please put the cordless handset back on the charger.
Compound of 子 (child, subsidiary) and 機 (machine, device). The term follows the pattern of 親機 (parent device) for the main unit.