Corporate Identity Design focuses on the needs of the company and brings enterprise business solutions to present the company as a corporate company.
Branding Design focuses on the emotional contact of the brand between potential customers, consumers, businesses and the brand.
If you have a different brand name and company name, before you choose any of the product above, you need to consider the one you wish to give priority. If you are planning to keep it fully professional, you must pick both products at the same time.