There is no difference. Medium-sized restaurants are the result of subdivision of catering services. In the past, catering services included everything, but now after subdivision of catering services, medium-sized restaurants are only one of them, so there is no difference.

a business license is a certificate issued by the administrative department for industry and commerce to industrial and commercial enterprises and individual operators to engage in a certain production and business activities. Its format shall be uniformly stipulated by the State Administration for Industry and Commerce.

its registered items are: name, address, person in charge, amount of funds, economic component, business scope, business mode, number of employees, business term, etc. The business license is divided into original and duplicate, both of which have the same legal effect.

the original should be placed in a conspicuous position in the company's domicile or business premises, and the business license shall not be forged, altered, leased, lent or transferred.

industrial and commercial enterprises or individual operators without business licenses are not allowed to start business, carve official seals, sign contracts, register trademarks or advertise, and banks are not allowed to open accounts.

Reference: Baidu Encyclopedia-Business License