A subsidiary is a company where another company (that is the parent company) has more than 50% shareholding. The subsidiary has more identity in terms of capital, asset base, own shareholding pattern, balance sheet profiles etc. compared to a branch. In this respect subsidiary has more independence compared to a branch of the parent company. From the angle of regulation and laws, the subsidiary will be treated as an independent entity. But the control of it lies with the parent company.
In the case of subsidiaries of foreign companies in India, they are locally incorporated and have their own capital base and their own local board of directors.