NBFC are companies other bank which are doing financial business. Before 1998-99 what used to happen was that many dishonest people used to form companies under the Companie Act , to carry on the business of financing. They accepted deposits from public and then flew away, as there were no controlling authoriy (like RBI as in the case of Banks). This prompted government to create an another category of companies called NBFC. Now if any company (other than Banking compay- which are also regulated by the Banking Regulation Act) want to do any business related with banking i.e. accepting of deposits and lending money or financing assets etc. then it has to get approval from RBI and such companies are referred to as NBFC.
In short we can say NBFC are companies i) Registered under companies Act &
ii) They also have to obtain approval from RBI and are thus
have to follow RBI guidelines and Prudential norms.
Apart from Banks and NBFC there are also some partnership firm engaged in the business of finance, like Muthoot Finance. Such Partnership Finance firms are not regulated by RBI.
So as far as your query is concerned, the business of an NBFC is similar to a bank only the regulatory setup is different.
There is no restriction that an NBFC can not give loan to a partnership firm.