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A company register is a register of organizations in the jurisdiction they operate under
A statistical business register has a different purpose than a company register. While a commercial/trade register serves a purpose of protection, accountability and control, a statistical register plays a central part in a system of official economic statistics at a national statistics office.
Basically, if you're doing any business are required to register such business either as a Company or a Firm or an LLP (Limited Liability Partnership). Instead of going for company registration, you could register the business as a Sole proprietorship.