Companies can be classified on the basis of the following:
1. Based on the Mode of Incorporation
Companies can further be of three types on the basis of modes of incorporation:
i) Royal Chartered Companies: These companies don’t exist any more. These are the companies created by a Royal Charter (monarchs and kings).
ii) Statutory Companies: Incorporated by means of special act by centre or state legislature.
iii) Incorporated Companies: These are companies registered under the companies act.
2. Based on the Number of Members
Companies can further be of three types on the basis of number of members:
i) Public Limited Company: Existence of a Public Limited Company is seperate from that of its shareholders. There need to be a minimum of 7 members to form a public limited company.
ii) Private Limited Company: More than 2 and less than 50 members are required for a private limited company. Here shares are subscribed by its members only and subscription is not open to general public.
iii) One Person Company: Only a single person is allowed to register a company under the one person company category.
3. Based on Liability of the Members
Companies can further be of three types on the basis of member liability:
i) Limited by shares: Liability of shareholders is limited to the amount they have invested.
ii) Limited by guarantee: On liquidation, shareholders have to pay the amount guaranteed by them.
iii) Unlimited companies: No limit on the liability of the shareholders.
Here is a link to an article for better understanding: https://www.feedough.com/types-of-companies/