NBFC:

Section 45I of the Reserve Bank of India Act, 1934 defines non-banking financial company:

A Non-Banking Financial Company (NBFC) is a company registered under the Companies Act, 2013 involved in the principal business of advancing loans, acquisition of shares/stocks/bonds/debentures/securities issued by Government or local authority or other marketable securities of a like nature, leasing, hire-purchase, insurance business, chit business. NBFC does not include any institution whose principal business is that of agriculture activity, industrial activity, purchase or sale of any goods (other than securities) or providing any services and sale/purchase/construction of immovable property.

A non-banking institution which is a company and has principal business of receiving deposits under any scheme or arrangement in one lump sum or in installments by way of contributions or in any other manner, is also a non-banking financial company.

Now the main question is that, what does conducting financial activity as principal business mean?

For that, RBI has set criteria to determine the financial activity as principal business of a company:

It says,
When the financial assets of the companies comprise of more than 50 % of the total assets and the income from financial assets amounts more than 50 % of the gross income. The criteria of income/assets are cumulative, that is, both the tests are required to be satisfied simultaneously as the determinant factor for principal business of a company.
If the company falls under this test, then we can say that, that the company conducts its financial activity as principal business. This is also called as 50-50 test.

Financial activity as principal business is necessary to constitute a NBFC, as per Section 45I of the Reserve Bank of India Act, 1934.

If a company falls under this test then, that company will be considered as NBFC. But, if a company does not fall into the above test, then it will not be considered as NBFC, then it will be considered as any other public or a private company. And according to Section 186 of the Companies Act 2013, a company can invest in securities.

According to Section 2(h) of the Securities Contracts (Regulation) Act, 1956:

The term securities include the following:

Shares, scrips, stocks, bonds, debentures, debenture stocks etc. in or of any incorporated company or another body corporate.
Derivatives.

• Units issued by any Collective Investment Scheme to the investors in such scheme.
• Security receipt as defined in Section 2(zg) of the Securitization and Reconstruction of Financial Assets and Enforcement of Security Interest Act, 2002.
• Units or any other such instruments issued to the investors under any Mutual fund scheme.

Government Securities
Such other instruments, rights or interest therein shall be declared by the government to be securities be declared by the government to be securities.

If a company has principal business of agriculture activity, industrial activity, buy or sale of any goods (other than securities) or providing any services and sale/buy/construction of immovable property and are doing some financial business(such as trading in derivatives) in a small way, then also a company cannot be said to be a NBFC.

As far as difference between trading and investing is concerned, there is no difference between trading and investing as per companies Act 2013.

Conclusion:
Yes, a company can trade in derivatives without being registered as NBFC. To constitute a NBFC, a company needs to go through a 50-50 test, if a company falls under this test then, that company will be registered as NBFC by RBI. But, if a company fails to comply with this test then, that company will not be registered as NBFC and can continue to trade in derivatives without being registered as NBFC Upto the limit specified by the RBI.