Parent company Brother/Sister concern Father/Mother company

Parent Company / Parent Corporation

A company can be called as the Parent company of another company, if that company:
- holds(owns) more than 50% shareholding or voting stock of that company; or
- controls the Board (Board of Directors) of that company either by electing directors or by way of its influence.

Example
(1) ABC Limited owns 53% shareholding in XYZ Limited. ABC Ltd is the parent company of XYZ Ltd.
(2) KPO Limited elects all the directors in BPO Limited. KPO Ltd is the parent company of BPO Ltd.

A.k.a

Parent companies are also referred to as Holding companies.


Mother Company

A Mother company has similar meaning like a Parent company.

A mother company owns a number of other companies, which may be in the similar line of business or totally other stream of business.


Sister Company / Sister Concern Company

When more than one company are under the management of a single company (a Parent company); they will be called as sister companies/ sister concerns to each other.

Example

DOG Limited is the parent company of RAT Limited and CAT Limited.
Hence, RAT Ltd and CAT Ltd are sister concerns or sister companies.

A.k.a.
Sister companies are generally known as the subsidiary companies of their parent company.

Note
Generally, sister companies, by its term, do not have any legal recognition/significance. But as a subsidiary company, these companies will have to comply with the rules and regulations prescribed for them.


Father Company

A Father company too has similar meaning like a Parent company. 

A father company is generally a company which owns one or more companies.


Brother Company

Brother company is not a popular term as compared to the above terms; hence it is very rare that two or more companies are referred as brother companies.

When two or more companies are run under the same group company, it could be called as brother companies.