Definition

Company means an association of persons incorporated under the Companies act with a separate legal entity and perpetual succession Whereas body corporate means a  legal entity  (such as an association, company, person, government, government agency, or institution) identified by a particular name. Also called corporation,  corporate body or corporate entity.

Section 2(11) of Companies Act 2013 provides that ‘body corporate’ or ‘corporation’ includes a company incorporated outside India, but does not include---

1. A cooperative society registered under any law relating to cooperative societies; and

2. Any other body corporate not being a company as defined in this Act), which the Central Government may, by notification, specify in this behalf.

General characteristics of body corporate are:

• Incorporated under some law

• Perpetual succession

• Ability to hold property in its own name

• Legal entity apart from the members

   

  Examples of ‘body corporates’:

   

1. All companies registered under Indian Companies Act
2. All companies registered under any Act outside India
3. Any Corporation registered under any special law in India or abroad
4. Public financial institutions u/s 2(72) of Companies Act 2013
5. Nationalised banks incorporated under Banking Companies (Acquisition & Transfer of Undertakings) Act 1970
6. LLPs

These are not bodies corporates:

1. Proprietorship concerns
2. Partnership firms (other than LLPs)
3. HUFs
4. Societies registered under Societies Registration Act
5. Mutual funds managed by trustees (UTI is a body corporate)

Thus body corporate is a wider term.  Every company is a body corporate but every body corporate is not a company.

I agree with PCA for giving more clarity.